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.
Madeleine Birchfield (May 18 2025 at 04:39):Apparently, the nLab now discourages the use of "evil" for (higher) categories that do not satisfy the principle of equivalence:
https://ncatlab.org/nlab/show/principle+of+equivalence#terminology
Notification Bot (May 18 2025 at 04:41):This topic was moved here from #learning: questions > nLab: the word "evil" by Madeleine Birchfield.
James Deikun (May 18 2025 at 06:30):This edit is due to someone named "Abe" who has only contributed to 24 pages on the nLab in only 2 sessions, I have a hard time taking it seriously as an official policy.
James Deikun (May 18 2025 at 06:42):It seems like a lot of their edits are concerned with removing the word "evil" even before that, and even in cases not connected with the principle of equivalence like the standard phrase "a necessary evil".
James Deikun (May 18 2025 at 06:50):OTOH the page discussion seems to indicate that Urs himself is ... unenthused by the use of "evil". I wish he'd made the edits himself if he's serious about this, though, as some of the edits made by "Abe" turned out quite awkward. (Not to mention making it look like the work of a troll.)
John Baez (May 18 2025 at 09:01):Trolls against evil.
Jade Master (May 18 2025 at 09:01):Good thing language is descriptive instead of prescriptive. I personally think it's a great word in this context :)
Nathanael Arkor (May 18 2025 at 09:21):There have been numerous discussions about how the word "evil" is unhelpful in the past few years; this is not new.
John Baez (May 18 2025 at 09:41):It's extremely non-new, but I enjoy it every time. /s
Madeleine Birchfield (May 18 2025 at 09:47):Abe's edits seems to have happened after this discussion:
https://nforum.ncatlab.org/discussion/11642/topos-theory/
In particular Urs Schreiber in his comment seems to imply that removing "evil" was already implicitly nLab policy.
Nathanael Arkor (May 18 2025 at 10:11):This has been Urs's stance for at least several years.
James Deikun (May 18 2025 at 10:48):TIL Urs is against "walking", as in the "walking arrow". I can understand "evil", but what's wrong with "walking"?
Nathanael Arkor (May 18 2025 at 10:58):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.
David Michael Roberts (May 18 2025 at 12:11):Personally I don't think the nLab should be so purified and purged so as to become wikipedia. I think it should record informal information/facts about the practice of category theorists that is not recorded on paper (or "in a book", so it can be cited, as D.P. suggested at the nForum thread). Category theory has enough bad folklore problems, the least that can be done is that this is documented for the future, because it will make things like forum discussions, mailing list discussions etc have more context.
David Michael Roberts (May 18 2025 at 12:13):I started this process by wanting to show my young daughter the nickname "Cats and Alligators" for the book by Freyd and Ščedrov, and found to my surprise the nLab didn't record this. I knew it from the categories mailing list, and were this not recorded somewhere, it would be lost to time, or else a mystery for anyone coming across it and not familiar with the appellation.
David Michael Roberts (May 18 2025 at 12:14):And then I thought that "Baby Elephant" which I guess I learned from @Todd Trimble also deserved recording. And then Urs got a bit puritan and thought it might mislead the young people....
David Michael Roberts (May 18 2025 at 12:15):(So where did Todd get it from?)
Madeleine Birchfield (May 18 2025 at 12:37):David Michael Roberts said:
Personally I don't think the nLab should be so purified and purged so as to become wikipedia. I think it should record informal information/facts about the practice of category theorists that is not recorded on paper (or "in a book", so it can be cited, as D.P. suggested at the nForum thread). Category theory has enough bad folklore problems, the least that can be done is that this is documented for the future, because it will make things like forum discussions, mailing list discussions etc have more context.
Unfortunately, the issue of anonymous editors adding their speculative original research to the nLab in recent years has annoyed a lot of nLab editors (see the nForum discussions on propositional resizing and (infinity,1)-coproduct) and has lead to an informal policy of citations being required for additions to the nLab, which we eventually made explicit on the nLab's HomePage. This does mean that some things that are folklore won't be put on the nLab since it hasn't been written down yet.
Nathanael Arkor (May 18 2025 at 14:03):David Michael Roberts said:
Personally I don't think the nLab should be so purified and purged so as to become wikipedia. I think it should record informal information/facts about the practice of category theorists that is not recorded on paper (or "in a book", so it can be cited, as D.P. suggested at the nForum thread).
The usage of "evil" is still recorded on the nLab page, it is just no longer encouraged on other pages. I think the nLab has a responsibility, as an influential source, not to propagate misleading terminology.
Nathanael Arkor (May 18 2025 at 14:04):David Michael Roberts said:
And then I thought that "Baby Elephant" which I guess I learned from Todd Trimble also deserved recording. And then Urs got a bit puritan and thought it might mislead the young people....
I think this is a different point of contention to "evil".
Notification Bot (May 18 2025 at 16:36):A message was moved here from #community: discussion > the word "walking" in category theory by Madeleine Birchfield.
Patrick Nicodemus (May 18 2025 at 20:42):I've had some really strange discussions about what constitutes evil. Several months ago I talked to a mathematician who was convinced that the standard argument that every category with products and equalizers has limits was evil because the argument goes:
and he argued that step 2 was evil because speaking about the set of objects of a category is evil because the set of objects of a category is not invariant up to isomorphism under equivalence of categories.
Patrick Nicodemus (May 18 2025 at 20:44):Seems like everybody's sick of this discussion but if the principle of invariance is being discussed in a way that makes people think standard arguments like this are somehow "bad" then there's certainly a communication problem somewhere.
Jonas Frey (May 18 2025 at 21:17):Interesting point! I think to construct limits from set-products and equalizers in the invariant / univalent setting, one has to assume that the groupoid core of the index-category admits a cover by a set, which is a kind of choice principle. This cover allows to replace the univalent index category by a weakly equivalent strict one.
Alternatively, you could demand groupoid indexed products instead of set-indexed products to obtain a constructive & invariant statement.
Ryan Wisnesky (May 18 2025 at 23:19):I've seen this too in type theory, where we often want to say "let A*B be the product of A and B" rather than "a product of A and B", and so talk about "categories equipped with choices of products" rather than categories with products and so on in order to make the "evil" explicit.
David Michael Roberts (May 19 2025 at 02:28):Nathanael Arkor said:
David Michael Roberts said:
And then I thought that "Baby Elephant" which I guess I learned from Todd Trimble also deserved recording. And then Urs got a bit puritan and thought it might mislead the young people....
I think this is a different point of contention to "evil".
It was Urs who brought up the example of the term of art "evil"
In the past these kinds of lame jokes have already caused us a good deal of work to get rid of them (like the notorious “evil”, “walking” and, yes, the habit of one contributor to reference Elephants).
I don't think a fun nickname of a book is in the same class at the term "evil" in many ways.
Madeleine Birchfield (May 19 2025 at 03:36):David Michael Roberts said:
I don't think a fun nickname of a book is in the same class at the term "evil" in many ways.
Yes, one of them being that "Baby Elephant" is folklore, while "evil" is an actually defined term in the category theory literature.
Todd Trimble (May 19 2025 at 04:52):David Michael Roberts said:
(So where did Todd get it from?)
I don't remember. I thought at first, reading this discussion, that maybe I got it from Toby Bartels, but that name hasn't come up in the nLab discussion that was linked here. But I can assure everyone that I didn't make it up. I think it must be folklore. People at the Categories list would probably know.
(I also didn't know I was in the "habit" of using the term "Baby Elephant". I guess I've sometimes used it in the company of people I feel comfortable around. It's true I used to feel a lot more comfortable at the nLab.)
As far as I know, both "evil" and "walking" originally come from James ("Jim") Dolan, and John Baez helped to propagate the term. Jim is in the habit (and I think "habit" is fair here) of inventing whimsical terms for mathematical ideas; these two are the most widely known, I guess.
This stuff happens. Some decades ago, topologists introduced "surge" as a verb to mean doing surgery on manifolds and the like. [I think I learned this from my old topology professor, Julius Shaneson.] Probably it was fun in the beginning. I don't know how it is now.
If anyone cares about my opinion: I think it's fine, in fact good, if the nLab includes mention of these terms in a descriptive context, just as dictionaries do. I also think it's fine if the nLab includes, alongside that, a usage note which can say that "evil" for example is widely deprecated -- similar to what many dictionaries do. That to me would be the most educational stance to take.
Personally, I've grown a little tired of "walking". I don't find it very strong, as whimsy goes. While I might continue to use it around people I know who know it as well, its obsolescence wouldn't bother me. But that doesn't mean the nLab shouldn't record it -- just as dictionaries continue to record archaisms.
"Cats and Alligators" is due to Freyd himself, I believe.
Madeleine Birchfield (May 19 2025 at 04:59):Todd Trimble said:
I also think it's fine if the nLab includes, alongside that, a usage note which can say that "evil" for example is widely deprecated -- similar to what many dictionaries do.
The thing is that in this case, "evil" clearly isn't deprecated, since there are publications in category theory within the past few years using "evil" for precisely this notion, and category theorists on this very thread saying that they use "evil" today. It's purely because Urs Schreiber and other nLab editors don't like using "evil" in the nLab for this sense because of the moral implications that the note got added to the page.
I personally don't like the word "evil" myself, but if it's currently being used in the literature, I don't see the need for a blanket ban on "evil" in the nLab.
Madeleine Birchfield (May 19 2025 at 05:11):Todd Trimble said:
If anyone cares about my opinion: I think it's fine, in fact good, if the nLab includes mention of these terms in a descriptive context, just as dictionaries do.
Well, the nLab is now requiring references to the literature for the material on the nLab, something that wasn't the case a decade ago. That's why "evil" is still mentioned in [[principle of equivalence]], while "baby Elephant" was removed from [[Topos Theory]].
David Michael Roberts (May 19 2025 at 05:20):I agree with "Cats and Alligators", he used it on the categories mailing list.
I also agree with the nLab taking a descriptive approach here.
The reason "evil" was stopped was because people outside category theory didn't take the term as a technical descriptor, with a mildly joking origin, but as a value judgement (or an implicit value judgement) on their way of mathematical working. It was in my memory becoming a source of professional friction because the nLab was spreading knowledge of the (somewhat) insider term much more widely than previously. Certainly the meme-quality commentary you got about the nLab didn't dissuade this (cf the old wording on "moduli stack of elliptic curves" page, with it's definition as "a [[moduli stack]] of [[elliptic curves]]").
David Michael Roberts (May 19 2025 at 05:22):I don't think the nLab should require references for everything on it. I don't want cranks there, but if we cannot include folklore, then the nLab is propagating the problem of in-crowd-only knowledge. There are many many many things on the nLab that are sourced to books or papers. Not least a lot of stuff Urs wrote himself.
Madeleine Birchfield (May 19 2025 at 05:25):That's the thing, the current attitude towards folklore and any other original research on the nLab is "go write a paper on the subject and put it on the arXiv / get it published, then we can add the folklore to the nLab and cite your paper in the article."
Because there's no way to distinguish between folklore and cranks to non-experts. That's how a lot of original research stayed on the nLab for years. Some anonymous editor was adding type theory original research to the nLab, and as a non-expert Urs Schreiber just assumed it was folklore from the type theory community, until actual type theorists got involved in an nForum discussion and pointed out that no, these concepts don't actually exist there.
The same problem would occur if a descriptive set theorist or an astrophysicist joined the nLab and started adding folklore from their respective fields. I don't see why category theory should get a pass on folklore.
Kevin Carlson (May 19 2025 at 05:41):The core of the folklore problem is that lots of folklore is interesting enough to be worth putting somewhere online, but not interesting enough to get a publication. Putting it on nLab is a couple of orders of magnitude lower a barrier to entry than putting it into a paper, and there's a clear reason why category theory might get a pass: the main nLab maintainers are, in fact, category theory experts. I can see how there are problematic cases here but it remains the case that if I come up with some good folklore that really doesn't have a literature reference, I'm going to put it on the nLab. And I don't particularly expect anyone to act to prevent that.
Madeleine Birchfield (May 19 2025 at 05:49):These days, Urs Schreiber and plenty of other nLab editors might act to prevent that. As we see with the case of "Baby Elephant" in [[Topos Theory]].
The modern nLab is not the same nLab that it was a few years ago.
Amar Hadzihasanovic (May 19 2025 at 06:17):How does the renaming of "computational trinitarianism" into "computational trilogy" fit into this? It's an example of terminology that comes from the literature, spread because it is widely seen as an apt metaphor for the concept it was portraying, and for what I can see was changed into a poorer and made-up version because Urs personally did not like it. Seems hard to claim that there is a "principled" policy towards these changes when something like this can happen.
Madeleine Birchfield (May 19 2025 at 06:30):If I read correctly, according to the article, "computational trilogy" comes from the Melliès reference from 2006?
Madeleine Birchfield (May 19 2025 at 06:32):But I would agree with renaming the page back to the original "computational trinitarianism" because it is the name more commonly used in the literature.
Madeleine Birchfield (May 19 2025 at 06:36):Huge discussion on the nForum from a few years ago about the title
https://nforum.ncatlab.org/discussion/4175/#Item_60
Judging by Mike Shulman's comments in the discussion, the rename happened before the nLab adopted stricter citation policies.
Kevin Carlson (May 19 2025 at 06:41):Madeleine Birchfield said:
These days, Urs Schreiber and plenty of other nLab editors might act to prevent that. As we see with the case of "Baby Elephant" in [[Topos Theory]].
Urs didn't actually act to prevent this, as you can see by looking at the discussion page. He voted against including it for a range of reasons, none of which were related to existence of citations. Then Dmitri Pavlov proposed breaking the stalemate by leaning on the literature, and somebody posting as Stanley Baldwin took it upon themselves to make the corresponding change. None of this is particularly important in itself, but it's edifying for revealing the difficulties inherent to running something as large as the nLab with such limited explicit agreement on principles or any process for producing such agreement. But it's also unavoidable for a project as small as the nLab in that there's really only a handful (even a singleton) of people doing the vast majority of the editing, so there's not the social juice available to do something more structured.
Kevin Carlson (May 19 2025 at 06:41):All in all, I continue to doubt that anybody would stop me if I put up a cool category theory fact that I don't have a reference for.
Madeleine Birchfield (May 19 2025 at 06:45):Kevin Carlson said:
All in all, I continue to doubt that anybody would stop me if I put up a cool category theory fact that I don't have a reference for.
Just don't advertise it on the nForum like David Roberts did and it is very unlikely Urs Schreiber or any other editor would notice. That's how anonymous editors were able to get away with their original research posting on the nLab for years.
Amar Hadzihasanovic (May 19 2025 at 06:49):Madeleine Birchfield said:
If I read correctly, according to the article, "computational trilogy" comes from the Melliès reference from 2006?
Melliès speaks of a "trilogy of concepts", but the phrase "computational trilogy" does not appear.
Madeleine Birchfield (May 19 2025 at 06:50):Yeah, I just finished reading the article and came to the same conclusion. I posted about it on the nForum:
https://nforum.ncatlab.org/discussion/4175/computational-trilogy/
David Michael Roberts (May 19 2025 at 06:59):Even without me having been a member (being a member?) of the nLab steering committee, this is why I think it is a good idea to have. I do not think one person's personal hangups and relatively minor additions like mine should cause some enormous cascade effect whereby a random bystander account starts rules lawyering and removing every hint of transgression of what is a rule designed for nLab sanitation from cranks, not turning us into hardnosed Wikipedia editing factions.
Urs got frustrated with the process, and decided to quit the committee, and since he owns the domain and is the largest contributor, still has the say. But quitting the committee to me feels like declining the responsibility and power to make decisions. There were issues around the actual software and infrastructure at play, I think, not about content. But I may be misremembering and also don't have the energy or desire to go and check.
Madeleine Birchfield (May 19 2025 at 07:12):David Michael Roberts said:
Urs got frustrated with the process, and decided to quit the committee, and since he owns the domain and is the largest contributor, still has the say.
Isn't that the whole problem - Urs Schreiber has all the power, and so if any editor does something Urs Schreiber likes, he will just allow the editors to continue doing whatever they are doing.
I remember back in 2022 when Urs Schreiber and Todd Trimble were on the opposite sides of this issue - Todd Trimble was arguing for citations in the literature for the original research being put on the nLab, while Urs Schreiber was defending the anonymous editors' contributions to the nLab. And because Urs Schreiber had the final say, nothing happened and the anonymous editors were allowed to spread their original research around the nLab.
David Michael Roberts (May 19 2025 at 07:21):Oh, the irony
Madeleine Birchfield (May 19 2025 at 07:23):Yes, it is very ironic. Eventually the anonymous editors became too annoying and disruptive for Urs Schreiber himself too and he slowly changed his opinions to the other side.
Madeleine Birchfield (May 19 2025 at 07:54):It was in 2021, not 2022, but here is the original discussion:
https://nforum.ncatlab.org/discussion/12983/#Item_9
Nathanael Arkor (May 19 2025 at 08:25):This topic perhaps deserves its own thread, but if people object to Urs's control of the nLab, the only reasonable solution as I see it is to start a new project.
Madeleine Birchfield (May 19 2025 at 09:32):Personally I don't really care about Urs Schreiber's ownership of the nLab, though I do see how people who want to add category theory folklore to the nLab might have an issue with Urs Schreiber if his ownership means that they can no longer add folklore like they used to be able to in years past.
John Baez (May 19 2025 at 09:49):The folklore issue is a bit curious, because isn't there a vast amount of unsourced claims on the nLab?
Jonas Frey (May 19 2025 at 09:50):I was about to say, the discussion is not really about category theory folklore. We're not talking theorems here.
Madeleine Birchfield (May 19 2025 at 09:57):Right, it's about terminology in this case.
Todd Trimble (May 19 2025 at 10:59):The thing is that in this case, "evil" clearly isn't deprecated
Madeleine, I absolutely refuse to get drawn into a long discussion about this. My name was mentioned; David wondered why I thought a certain way; I gave an answer, and added facts that I believe are relevant.
Madeleine, please do attend to what I say. I said widely deprecated. That's just a fact. There are many people who find the terminology downright offensive and have said so loudly and publicly (to deprecate means to express disapproval). A good usage guide, which I think is a legit function for the nLab, would make a note that certain usages are considered offensive or in poor taste or whatever by certain people in certain contexts.
In particular, I did not say universally deprecated.
Madeleine Birchfield (May 19 2025 at 11:01):Actually, this may just be me misreading "deprecated" as "depreciated". Sorry.
Todd Trimble (May 19 2025 at 11:02):Okay, thanks. That makes sense then.
Morgan Rogers (he/him) (May 19 2025 at 11:16):Todd Trimble said:
The thing is that in this case, "evil" clearly isn't deprecated
Madeleine, please do attend to what I say. I said widely deprecated. That's just a fact. There are many people who find the terminology downright offensive and have said so loudly and publicly (to deprecate means to express disapproval).
To be fair to Madeleine, I have only ever seen the word "deprecate" used in a computing context to mean outdated; see this answer or the third definition here, with the exception of the phrase "self-deprecating" to refer to humour targeting oneself. I shared the confusion.
Todd Trimble (May 19 2025 at 11:19):I don't mean to give offense saying this, but to me this is a common word. It's used very often in dictionaries.
Anyway, glad the confusion got cleared up.
Madeleine Birchfield (May 19 2025 at 11:21):Morgan Rogers (he/him) said:
To be fair to Madeleine, I have only ever seen the word "deprecate" used in a computing context to mean outdated; see this answer or the third definition here, with the exception of the phrase "self-deprecating" to refer to humour targeting oneself. I shared the confusion.
That was definitely where I got my use of "deprecate" from then. I used to do programming back in the day and every once in a while one of the libraries I used got an update that said that XYZ feature is now deprecated - meaning it was outdated and soon won't be supported anymore. And so I interpreted Todd Trimble's comment as "the use of 'evil' is outdated" and I'm like no it isn't, it's currently being used in papers to this day.
Madeleine Birchfield (May 19 2025 at 11:29):Anyways, I don't really have anything else to say about the topic of "evil" either.
Morgan Rogers (he/him) (May 19 2025 at 11:33):Out of curiosity I checked Google's n-gram viewer to find out the prevalence of some synonyms of deprecate.
image.png
It seems that since around 2003, "disfavored" has been increasingly disfavored, while "deprecated" is becoming deprecated. Based on this graph, you could avoid being disparaged by using "disparaged" @Todd Trimble :stuck_out_tongue_wink: (For more amusement, I also discovered that use of the (actually unrelated) word "depreciated" has depreciated steadily over the last century.)
Todd Trimble (May 19 2025 at 11:49):"disfavored" has been increasingly disfavored
I think you meant "increasingly favored", right? :-)
Anyway, I had no idea that I would be misunderstood. Even though I prefer "deprecate" in the context of usage notes in dictionaries and such, I'll try to remember this.
Patrick Nicodemus (May 19 2025 at 17:30):Well, in a programming library the authors have the ultimate authority, they can set that convention unilaterally for the community - stop using this - because they will enforce it by removing it in 2 years. So I think the issue is that if a programmer hears "deprecate" they understand it with the same level of force as if it was unilaterally agreed by an authority, i.e., it is widely agreed that this practice should stop and will soon be phased out, rather than that there is a large minority who verbally oppose it.
Matteo Capucci (he/him) (May 20 2025 at 21:02):James Deikun said:
I wish he'd made the edits himself if he's serious about this,
If only Urs put more time into the nLab..! :rolling_eyes:
Madeleine Birchfield (Jun 03 2025 at 22:07):James Deikun said:
OTOH the page discussion seems to indicate that Urs himself is ... unenthused by the use of "evil". I wish he'd made the edits himself if he's serious about this, though, as some of the edits made by "Abe" turned out quite awkward. (Not to mention making it look like the work of a troll.)
Abe tried adding a similar note for the use of "Ass" to the newly created article [[assembly]] and got reprimanded by Urs Schreiber. Abe's note got removed from the assembly article by a George Harrison for not being official nLab policy. George Harrison said the nLab should wait until Urs Schreiber makes a decision before adding notes. Urs Schreiber then said, in the same comment he reprimanded Abe, not to worry about the names.
https://nforum.ncatlab.org/discussion/19305/assembly/#Item_0
So then what was the big deal with "evil" and "walking" that warranted a note to be added to [[principle of equivalence]]?
Todd Trimble (Jun 04 2025 at 00:38):So then what was the big deal with "evil" and "walking" that warranted a note to be added to [[principle of equivalence]]?
I think that note (at [[principle of equivalence]]) was added by Abe, revision 108. What was there before was a lot less heavy-handed, and I don't think the additional note was really warranted (bringing up "nLab policy", on an nLab page that is supposed to be about mathematics, reads very awkwardly to me).
David Michael Roberts (Jun 04 2025 at 01:53):I agree that stating nLab policy is awkward, and merely stating which usage nLab pages will use, when there is a choice, is perfectly descriptive, rather than proscriptive.
Madeleine Birchfield (Jun 04 2025 at 03:35):Todd Trimble said:
I think that note (at [[principle of equivalence]]) was added by Abe, revision 108. What was there before was a lot less heavy-handed, and I don't think the additional note was really warranted (bringing up "nLab policy", on an nLab page that is supposed to be about mathematics, reads very awkwardly to me).
Abe added the note after Urs Schreiber made this comment on the nForum:
https://nforum.ncatlab.org/discussion/4201/principle-of-equivalence/?Focus=122402#Comment_122402
Todd Trimble (Jun 04 2025 at 04:37):But Urs didn't tell him to write those words. (Urs's opinion on the subject has been known a long time.)
(It appears some people regard Urs as king of the nLab, and take his wishes as their commands.)
Madeleine Birchfield (Jun 04 2025 at 10:54):Looks like the note on principle of equivalence was also removed as well:
https://ncatlab.org/nlab/revision/diff/principle+of+equivalence/112