You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
James Deikun (May 18 2025 at 12:30):TBH I find the adjective "free-standing" does not cover everythign "walking" does. Is the "walking monoid" really "free-standing" when it includes a whole monoidal category?
Madeleine Birchfield (May 18 2025 at 12:51):Nathanael Arkor said:
I'm not sure about the context for that, but I also think "walking" isn't particularly good terminology (though for different reasons than "evil"). My impression is that James Dolan's usage of "walking" is very colloquial, and I think most English speakers would not find the usage obvious. In contrast, I think an adjective like "free-standing" is much clearer.
Aren't walking structures the initial such structures in the bicategory of categories? (i.e. the walking arrow is the initial category with two objects and a morphism from one object to the other, the walking isomorphism is the initial category with two objects and an isomorphism from one object to the other, etc...)
James Deikun (May 18 2025 at 13:48):If we want to use precise terminology based on "initial", "walking X" becomes "initial <something> containing an X" ... which is quite a mouthful.
Jonas Frey (May 18 2025 at 13:50):Madeleine Birchfield said:
Aren't walking structures the initial such structures in the bicategory of categories? (i.e. the walking arrow is the initial category with two objects and a morphism from one object to the other, the walking isomorphism is the initial category with two objects and an isomorphism from one object to the other, etc...)
While it is true that generic objects are initial in certain categories, this doesn't adequately capture the universal property.
The universal property of the generic (walking/free-standing) monoid, for example is that it (bi)represents the 2-functor
which sends every monoidal category to its category of internal monoids.
Now the important thing is that contrary to (co)presheaves of sets, representability of (co)presheaves of categories is not characterized by initiality/terminality. What you can characterize by bi-initiality i representability of the underlying presheaf
of groupoids, and the generic monoid will be bi-initial in its (2,1)-category of elements, but that doesn't capture the fact that homming out of the generic objects gives categories of algebras, which is central to functorial semantics.
Jonas Frey (May 18 2025 at 13:56):I like to emphasize that whenever people talk about "initiality" in the context of syntactic categories of type theories, although there the "initiality" POV is often justified since people are typically interested in representing Set-valued functors, and in particular one is normally not interested in non-invertible morphisms between models of a type theory in the same category.
Jonas Frey (May 18 2025 at 14:02):Regarding terminology: I used "generic" above, but I think "universal" also makes sense since one also speaks of universal elements of (co)presheaves in the context of representability.
Nathanael Arkor (May 18 2025 at 14:07):Madeleine Birchfield said:
Aren't walking structures the initial such structures in the bicategory of categories?
Essentially yes, though there are some subtleties (the structure in which initiality is considered is often left implicit, but is not always the 2-category of categories). But this doesn't have bearing on terminology: the term "free-standing" also serves this function.
Nathanael Arkor (May 18 2025 at 14:08):James Deikun said:
TBH I find the adjective "free-standing" does not cover everythign "walking" does. Is the "walking monoid" really "free-standing" when it includes a whole monoidal category?
A monoid (in this context) is by definition defined with respect to a monoidal category, so it wouldn't make sense for "free-standing" to mean anything else.
Nathanael Arkor (May 18 2025 at 14:11):Jonas Frey said:
Now the important thing is that contrary to (co)presheaves of sets, representability of (co)presheaves of categories is not characterized by initiality/terminality. What you can characterize by bi-initiality is the underlying presheaf
of groupoids, and the generic monoid will be bi-initial in its (2,1)-category of elements, but that doesn't capture the fact that homming out of the generic objects gives categories of algebras, which is central to functorial semantics.
The "free-standing monoid" is 2-initial in the 2-category of monoidal categories equipped with a monoid.
Jonas Frey (May 18 2025 at 14:13):Nathanael Arkor said:
Jonas Frey said:
Now the important thing is that contrary to (co)presheaves of sets, representability of (co)presheaves of categories is not characterized by initiality/terminality. What you can characterize by bi-initiality is the underlying presheaf
of groupoids, and the generic monoid will be bi-initial in its (2,1)-category of elements, but that doesn't capture the fact that homming out of the generic objects gives categories of algebras, which is central to functorial semantics.The "free-standing monoid" is 2-initial in the 2-category of monoidal categories equipped with a monoid.
Yes, but this doesn't fully capture its universal property! The universal property is that it represents a co-presheaf of categories, not only of sets/groupoids!
Nathanael Arkor (May 18 2025 at 14:37):I take your point. But it is also addressed by replacing "2-category" with "double category", so I think it is still reasonable to say that free-standing structures are, by definition, initial such structures.
Jonas Frey (May 18 2025 at 15:07):Nathanael Arkor said:
I take your point. But it is also addressed by replacing "2-category" with "double category", so I think it is still reasonable to say that free-standing structures are, by definition, initial such structures.
Ahh I was wondering about a double categorical account of this!
So what's the statement? A co-presheaf of categories is representable iff its double category of elements has an element which is "double initial" in the sense that for every object there is a unique horizontal arrow, and for each vertical arrow there is a unique triangle with the horizontal arrows?
Do you have a reference for that?
Nathanael Arkor (May 18 2025 at 15:33):A version of the statement appears as Theorem 6.8 of clingman and Moser's Bi-initial objects and bi-representations are not so different.
Jonas Frey (May 18 2025 at 15:38):Great, thanks so much!
Notification Bot (May 18 2025 at 16:35):24 messages were moved here from #community: discussion > nLab: the word "evil" by Madeleine Birchfield.
Patrick Nicodemus (May 18 2025 at 20:57):I have never understood the name walking. Can someone point me to non-categorical use of "walking" where it is used the same way as the categorical sense? Not challenging it, just saying I'd like to see where the term comes from - a few English sentences where "walking" is used to mean "prototypical" or "quintessential"
Something like "Andrew Carnegie, the walking capitalist".
Nathanael Arkor (May 18 2025 at 21:49):The origin of the terminology is explained here.
Amar Hadzihasanovic (May 19 2025 at 06:23):That's funny, I had a completely different headcanon for its origin. In Italian we use a word meaning "walking" for what in English is "travelling" as in "travelling salesman". So I assumed that the walking monoid was the monoid that would visit all the different "homes", whenever they need a monoid.
Amar Hadzihasanovic (May 19 2025 at 06:24):("Travelling salesman" = "venditore ambulante" = "walking salesman")
Amar Hadzihasanovic (May 19 2025 at 06:26):"You need a monoid? Order a functor directly to your home from the walking monoid".
David Michael Roberts (May 19 2025 at 06:54):If Conway can name things in whimsical ways, and people talk about the concept seriously even though the name is silly to a non-expert, I don't see why Jim Dolan can't do the same.
Nathanael Arkor (May 19 2025 at 07:00):It's not about permission: it's about descriptiveness. It's better to have a name that conveys intuition (and whose definition it is even possible to guess) rather than an obscure reference (or joke).
David Michael Roberts (May 19 2025 at 07:29):Well, without looking it up, what is a "thrackle"?
Madeleine Birchfield (May 19 2025 at 07:32):What's the intuition behind "field" and "monoid"?
David Michael Roberts (May 19 2025 at 07:55):What does syllepsis or syzygy mean?
Morgan Rogers (he/him) (May 19 2025 at 08:01):In defense of Nathanael's point: if you choose a common noun or adjective as a name for a concept, you should definitely take into account the common meaning. If you're willing to make up words or employ obscure ones, so much the better, since it enables non-specialists to identify a word as jargon, avoiding confusion.
Morgan Rogers (he/him) (May 19 2025 at 08:05):The ideal choice is a word obscure and/or concrete enough that one would not expect it to carry its usual meaning (if they know it) when mentioned in a mathematical context, but whose usual meaning does actually carry some of its intuition/meaning to the mathematical context. imo Grothendieck was good at coining these: sheaf and stalk come to mind.
Morgan Rogers (he/him) (May 19 2025 at 08:09):Words like group and set often suffer from having very common counterparts. I find myself having to be careful with describing collections to non-mathematicians or explicitly saying early on that these terms have technical meanings related to but not coinciding with their common meanings (in common usage they are synonymous, after all).
David Michael Roberts (May 19 2025 at 08:18):Things like [[heaps]] are also names in a less than useful way.
Nathanael Arkor (May 19 2025 at 08:21):David Michael Roberts said:
Well, without looking it up, what is a "thrackle"?
Aren't you just illustrating my point?
Nathanael Arkor (May 19 2025 at 08:23):I think "thrackle" is bad terminology too.
Nathanael Arkor (May 19 2025 at 08:24):I do think that in some cases, there isn't an obvious descriptive term (or the obvious descriptive term is too long to use practically for a common situation), and in that case it is sensible to invent a new term or to use an existing term in a way that won't cause confusion.
Madeleine Birchfield (May 19 2025 at 08:24):Another thing that is terrible: structures that are named as "[mathematician's surname] space".
Nathan Corbyn (May 19 2025 at 08:28):Morgan Rogers (he/him) said:
sheaf and stalk come to mind.
Although these words imply completely the wrong topology
Morgan Rogers (he/him) (May 19 2025 at 09:16):(fwiw "category" is pretty borderline by the above criteria. I had an instructive experience where I spent an hour discussing category theory with a friend only to realise that they had maintained the assumption that "category" was a formalisation of the common meaning of the word... be careful when choosing terminology, folks. For better or for worse, words mean things.)
Jonas Frey (May 19 2025 at 09:27):Nathan Corbyn said:
Morgan Rogers (he/him) said:
sheaf and stalk come to mind.
Although these words imply completely the wrong topology
Exactly! Moerdijk and Maclane's kebab metaphor is far superior since the cohesion is horizontal and not vertical!
Nathan Corbyn (May 19 2025 at 09:47):@Oscar Cunningham once suggested ‘baklava’ (in reference to the sheets of pastry that come together and split apart) which I also quite liked
Madeleine Birchfield (May 19 2025 at 10:17):James Deikun said:
TIL Urs is against "walking", as in the "walking arrow". I can understand "evil", but what's wrong with "walking"?
Looks like Urs Schreiber now accepts "walking" on the nLab:
https://nforum.ncatlab.org/discussion/7874/walking-structure/?Focus=122453#Comment_122453
Nathanael Arkor (May 19 2025 at 11:53):That comment reads to me as though Urs accepts that "walking" is used in the literature (though I agree with him that it certainly originated on the nLab), but that still leaves open the question as to whether it should be the term that the nLab uses (it should mention all options, but it is better to use a term consistently on other pages).
Todd Trimble (May 19 2025 at 11:58):though I agree with him that it certainly originated on the nLab
"Walking" originated on the nLab? Did you mean to say n-Cafe? It originated with Jim Dolan, and then propagated by John, I believe primarily at the Cafe. (I guess I should look all this up and give citations, but I'm feeling lazy at the moment.)
John Baez (May 19 2025 at 12:07):Yes, it originated with James Dolan, who explained it to me with the "he's a walking pair of eyebrows" joke. I then started using it, and now it seems people are arguing about whether it deserves to be canonized as official terminology.
I don't recall ever using it in a paper, except for my latest paper with Todd, where for example the first line of the abstract says
Settling a conjecture from an earlier paper, we prove that the monoid of matrices in a field of characteristic zero is the 'walking monoid with an -dimensional representation.'
John Baez (May 19 2025 at 12:10):I can't imagine using it without using scare quotes, because I don't think of it as standard mathematical terminology, more like something you'd say with a nudge and a wink.
(I like to use single quotes for scare quotes, I'm weird that way.)
Todd Trimble (May 19 2025 at 12:12):Oh! Maybe a citation should be supplied for that word?
John Baez (May 19 2025 at 12:28):In our paper???
Todd Trimble (May 19 2025 at 12:35):Yes, that is what I meant -- but the three question marks suggests you disagree.
After all the discussion of "evil" and "walking", I was just wondering whether that terminology would be confusing to readers. But if you don't think so, I won't be fussed about it.
John Baez (May 19 2025 at 12:38):Since it's in the abstract, which appears on the arXiv front page, a citation would be awkward. (Some people put footnotes in their abstracts, but I deprecate that practice.)
John Baez (May 19 2025 at 12:39):I don't think more people are confused by "walking" than by most other things mathematicians say and write, which generally tend to be quite confusing unless one happens to know the right stuff.
Todd Trimble (May 19 2025 at 12:40):I didn't mean in the abstract necessarily, but where it's first used in the body of the paper. Anyway, as I say, I'll happily let it go if you think it isn't worth it.
John Baez (May 19 2025 at 12:42):Maybe we could put in an explanation of the joke, buried in a footnote somewhere! That would be cute, but perhaps too cute. Right now we give two interpretations of what "walking monoid with an n-dimensional representation" could mean, a shallow one and a deeper one, and this may do better than any theoretical explanation of the general concept of walkingness, which is a bit slippery.
Todd Trimble (May 19 2025 at 12:44):Okay, that's fine then.
Amar Hadzihasanovic (May 19 2025 at 15:54):FWIW it's widely accepted enough in the homotopy theory/higher categories/derived algebraic geometry community that myself and three coauthors used it in the title of our recent paper and it never even came up in discussion that it was something worth thinking about
Amar Hadzihasanovic (May 19 2025 at 15:56):But my anecdotal experience is that "pure" category theorists spend more time thinking about whether a technical term is the best possible than most other mathematicians
Amar Hadzihasanovic (May 19 2025 at 15:56):Presumably because they are more used to thinking across all different instantiations of the same categorical structure
Amar Hadzihasanovic (May 19 2025 at 15:58):Typically nobody else is wondering whether some name's intuitive sense carries across all other structurally equivalent instances of that concept
John Baez (May 19 2025 at 16:44):These discussions about terminology make me wish I weren't a category theorist. Maybe it means I'm not. :smirk: I not only don't care about the outcome that much (it's not as if we're the official arbiters of terminology and our decision matters very much), I also find the whole business stressful... perhaps because what started as a light-hearded phrase James Dolan came up with is now treated with all the seriousness of a court case.
Patrick Nicodemus (May 19 2025 at 17:16):Nathanael Arkor said:
The origin of the terminology is explained here.
Okay, now I get it. I think in my experience this is usually used with the indefinite article "a".
I would say "He's a walking pair of eyebrows."
Google turns up hits for "He's a walking red flag", "He's a walking miracle", etc.
There is also a dictionary entry here.
Patrick Nicodemus (May 19 2025 at 17:17):Note that the dictionary definition uses the indefinite article "a". For me at least, this was enough to completely throw me off.
Patrick Nicodemus (May 19 2025 at 17:17):Amar Hadzihasanovic said:
"You need a monoid? Order a functor directly to your home from the walking monoid".
The successor delivery service to the wildly successful "You need a lemma?"
Kevin Carlson (May 19 2025 at 17:18):Patrick Nicodemus said:
I would say "He's a walking pair of eyebrows."
Well, you can handle that issue using the [[generalized the]], assuming we're agreed that any two people describable as a walking pair of eyebrows are canonically isomorphic.
Nathanael Arkor (May 19 2025 at 17:31):Todd Trimble said:
though I agree with him that it certainly originated on the nLab
"Walking" originated on the nLab? Did you mean to say n-Cafe? It originated with Jim Dolan, and then propagated by John, I believe primarily at the Cafe. (I guess I should look all this up and give citations, but I'm feeling lazy at the moment.)
I meant that I would wager that people used the term in papers because they found the term on the nLab and thought it well-established terminology. I doubt anyone would have used the term if it had only appeared on the n-Category Café.
Evan Patterson (May 19 2025 at 17:34):Right, I've been using the "walking" phrase for years (FWIW, I find it charming) and, like so much of what I know about category theory, I learned it from the nLab, or at least by following leads starting from the nLab.
Alex Kreitzberg (May 19 2025 at 17:38):I find "Walking X" charming and evocative as well
John Baez (May 19 2025 at 19:39):For people who like the "walking X", you'll be glad to hear we're soon going to roll out the "talking X".
Then you'll be able to take a monoidal category containing a monoid object and ask "it talks the talk, but does it walk the walk?"
Matteo Capucci (he/him) (May 20 2025 at 21:19):Nathanael Arkor said:
It's not about permission: it's about descriptiveness. It's better to have a name that conveys intuition (and whose definition it is even possible to guess) rather than an obscure reference (or joke).
though unless the name is seriously bad, I'd say changing established/well-understood terminology and thus polluting the namespace even more it's even worse than having a slightly undescriptive name. perfect is the enemy of good, and it's basically definitionally impossible to have perfect terminology.
incidentally I like the term 'walking', though 'generic' or '(co)classifier/classifying' is also good with me, but note they're basically equally obscure to someone who's not familiar with them (esp. to the non-native speakers, as Amar's account above witnesses).
Mike Shulman (May 20 2025 at 21:40):I believe Jaap van Oosten wrote that "The only thing worse than bad terminology is continually changing terminology."
Zoltan A. Kocsis (Z.A.K.) (May 21 2025 at 03:37):Madeleine Birchfield said:
Another thing that is terrible: structures that are named as "[mathematician's surname] space".
Having ruminated on this for a couple of days, I think I now disagree.
Compare the flexibility of Abelian and Cartesian with orthogonal or commutative: the former can pack a lot more connotations into a single word, without staying tied to set features.
This is useful since we don't necessarily know the most important feature when we assign an adjective to a class of objects.
Then there's productivity. Over time, "X " or "Xian" can turn into a tag for broader generalizations that grow from the original work. I don't think more descriptive names have the same flexibility: Abelian categories would never have been named commutative categories (indeed even symmetric monoidal categories, where commutative would be a better fit, are not called commutative), a more descriptive name for Frobenius automorphisms would have prevented the creation of Frobenioids, etc.
Other fields do this successfully too, see e.g. the adjective Dickensian, which is flexible enough to imply "poor social or working conditions" equally well as "a story with comically repulsive characters".
Nathanael Arkor (May 21 2025 at 05:59):Matteo Capucci (he/him) said:
though unless the name is seriously bad, I'd say changing established/well-understood terminology and thus polluting the namespace even more it's even worse than having a slightly undescriptive name. perfect is the enemy of good, and it's basically definitionally impossible to have perfect terminology.
That's not the case here: there are alternatives to "walking" that are also established and better understood, so using these terms does not add to the namespace.
Nathanael Arkor (May 21 2025 at 06:01):Zoltan A. Kocsis (Z.A.K.) said:
Compare the flexibility of Abelian and Cartesian with orthogonal or commutative: the former can pack a lot more connotations into a single word, without staying tied to set features.
How? If you use a single word for something, then you can convey the same connotations with whatever word you choose. A person's name isn't special as a word in this regard.
Nathanael Arkor (May 21 2025 at 06:06):Zoltan A. Kocsis (Z.A.K.) said:
Then there's productivity. Over time, "X " or "Xian" can turn into a tag for broader generalizations that grow from the original work. I don't think more descriptive names have the same flexibility: Abelian categories would never have been named commutative categories (indeed even symmetric monoidal categories, where commutative would be a better fit, are not called commutative), a more descriptive name for Frobenius automorphisms would have prevented the creation of Frobenioids, etc.
First of all, there's no reason that non-personal names cannot be used this way. Second, it is worth reflecting whether this is even desirable. I tend to find these situations unhelpful, because it involves overloading terminology in ways that can be confusing when you first encounter them. Third, I agree that a more descriptive name for Frobenius automorphisms may have not suggested the term "Frobenioid", but the way you phrase this makes it sound like "Frobenioid" is the ideal term, and we would have missed out if some other terminology was used. But this just isn't true: there's nothing objectively useful about "Frobenioid" compared to some other evocative choice of terminology.
Nathanael Arkor (May 21 2025 at 06:09):Zoltan A. Kocsis (Z.A.K.) said:
Other fields do this successfully too, see e.g. the adjective Dickensian, which is flexible enough to imply "poor social or working conditions" equally well as "a story with comically repulsive characters".
I don't understand your use of "successfully". One can literally use any word to mean anything, and if enough people follow your lead, it becomes standard. But this reflects relatively little on how good the choice of the word was. There's no reason "Dickensian" is any better a word than some other choice.
Mike Shulman (May 21 2025 at 06:41):Thanks for having the courage to say that, Zoltan! Sometimes I think mathematicians regard it as self-evident that eponyms are bad, when in fact there are arguments to be made for the other side.
Personally, I think most of the arguments for eponyms can be effortlessly generalized to argue for any (mathematical) neologisms. The point is, sometimes we really want a new name for something rather than to reuse some ones that already have meaning in mathematics. When we introduce a new word that doesn't previously have a mathematical meaning (whether or not it is an existing word in some natural language), we are free to define it to mean one specific thing, without the danger of confusion with other meanings of that word. And a new word can then also have its meaning expanded in turn over time to refer to other related things. If we never introduced any new words into mathematics, eventually all the mathematical words would be as overloaded as, say, "cartesian" is now, and things would be more confusing.
Naming things after a person is one way to get a new word into mathematics. But we can also import existing words from natural languages, or create new words that didn't exist before in any language. A couple such words that come to mind are "topos" and "operad".
David Corfield (May 21 2025 at 08:15):Mike Shulman said:
or create new words that didn't exist before in any language. A couple such words that come to mind are "topos" and "operad".
Except of course that the Greeks said, and still say, τόπος for place. But point taken.
David Michael Roberts (May 21 2025 at 08:29):we can also import existing words from natural languages, or....
David Michael Roberts (May 21 2025 at 08:29):I guess Mike gave one of each...
David Corfield (May 21 2025 at 09:04):Whoops. Sorry, Mike! Should read properly.
Antonio Lorenzin (May 21 2025 at 10:38):Mike Shulman said:
Sometimes I think mathematicians regard it as self-evident that eponyms are bad, when in fact there are arguments to be made for the other side.
I'd like to give an example of where this has clearly been the case, since it hits home: Markov categories vs affine CD-categories.
This brings me to an inherent problem about descriptiveness (since it seems no one has pointed it out yet): it can easily lead to weird acronyms that later on just lose their meaning. One example are CW-complexes. About this topic, I loved what Pedersen wrote in his book:
The original name CCR means “completely continuous representations” (completely continuous operators being another name for C(H)). The next layer in the hierarchy, “GCR” indicates a generalization of the CCR condition. The modern names “liminary” and “postliminary” do not mean anything that may be more aesthetic. In any case the Anglo-Saxon Habit of Condensing Every Formula into its Leading Characters (abbreviated ASHCEFLC) should not be tolerated in mathematics.
I also laugh a bit thinking about it, since the book is about -algebras (C stands for closed), which are a minimal (so I guess acceptable) example of the ASHCEFLC.
Nathanael Arkor (May 21 2025 at 10:54):Antonio Lorenzin said:
Mike Shulman said:
Sometimes I think mathematicians regard it as self-evident that eponyms are bad, when in fact there are arguments to be made for the other side.
I'd like to give an example of where this has clearly been the case, since it hits home: Markov categories vs affine CD-categories.
This is making a point that has been made already, but I think it worth repeating that "there exist non-eponymous terms that are bad" is not an argument in favour of eponymous terms, but rather against bad non-eponymous terms.
Nathanael Arkor (May 21 2025 at 10:55):It's certainly true that descriptive terms can lead to taxomonic terms that being unwieldy. This is typically the point at which a neologism becomes useful, as Mike pointed out.
Zoltan A. Kocsis (Z.A.K.) (May 21 2025 at 11:36):How? If you use a single word for something, then you can convey the same connotations with whatever word you choose. A person's name isn't special as a word in this regard.
Thanks for engaging. I think I explained above why and how eponyms function more productively (in the linguistic sense) than the alternatives.
If people had used the adjective "commutative" instead of "Abelian" in "Abelian group", we would not have later managed to create the term "commutative category" to stand in for what is now "Abelian category", because the connotations would not have matched. The same holds for _any_ other neologism based on properties of Abelian groups: if someone had coined "rearrangeable group" instead, we still could not have created "rearrangeable category", since rearrangeable would still carry the wrong connotations here. Had one gone by analogy with the integers, and called them "Integral groups", well, still wouldn't work.
Nobody had any hidden insight about what will have made the category of Abelian groups look especially interesting, not back when the term "Abelian group" was first used. But the word Abelian stayed useful, and kept developing, precisely because it had no other strictly mathematical connotations attached to it and could freely take on the ones it needed.
One could of course have coined a new term for Abelian categories, unrelated to Abelian groups, but it is useful to be reminded that the category of all abelian groups is an abelian category.
The only other words with similar flexibility include very abstract adjectives, like "ideal", "normal", "prime" or "simple" (many of them are overloaded, and have their own serious problems), and other proper names with no prior associations. But if the choice comes down to a totally random / tenuously related adjective as neologism ("brisk group", compare this very thread, which is about an adjective that wasn't even random just fell flat for many people) or totally irrelevant proper name ("Gaussian groups") or metonymy ("Danish groups", see the tropical geometry controversy) vs. some name that's historically related ("Abelian groups"), well, the one that acknowledges some actual connection seems like a clear winner to me.
Zoltan A. Kocsis (Z.A.K.) (May 21 2025 at 11:38):Antonio Lorenzin said:
I also laugh a bit thinking about it, since the book is about -algebras (C stands for closed), which are a minimal (so I guess acceptable) example of the ASHCEFLC.
The model theorists went all-in on something similar, NIP theories have "Not the Independence Property". :)
Antonio Lorenzin (May 21 2025 at 11:40):Nathanael Arkor said:
Antonio Lorenzin said:
Mike Shulman said:
Sometimes I think mathematicians regard it as self-evident that eponyms are bad, when in fact there are arguments to be made for the other side.
I'd like to give an example of where this has clearly been the case, since it hits home: Markov categories vs affine CD-categories.
This is making a point that has been made already, but I think it worth repeating that "there exist non-eponymous terms that are bad" is not an argument in favour of eponymous terms, but rather against bad non-eponymous terms.
The point I was trying to make with that example is: even the best descriptive choice may be worse than an eponym. After all, "affine CD" is describing specifically what you are requiring, maybe you could consider "total CD" if you have another perspective, but I do believe it is a good name overall.