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JR Learnstomath (Mar 18 2026 at 07:26):I came here from @David Egolf (he/him) 's "starting Zulip conversations", um, conversation: https://categorytheory.zulipchat.com/#narrow/channel/233322-practice.3A-communication/topic/starting.20Zulip.20conversations/with/580103849, because yet again, I've been able to take some tentative steps forward because of you -- thanks, David!
One of my earliest observations of math - this kind of math - is that it's naturally a team sport, and I really like that about it. So I'm nervous about this, but I'm going to cast a spell: sprobujemy ("let's try" in Polish) and give it a go.
I'll start this conversation by saying why I'm starting it, and why here in "community: our work", and then ask a few questions.
There's one meta-reason (M) and three subject-related reasons (S) why and why here:
(M1)I can't claim I'm "applying category theory", but I'm studying how to, and need a non-stream-of-information place to put what I'm learning because:
(M1a) This platform is overwhelming for me, and I'm a limited human with high cognitive loading. I also switch contexts dramatically, so I forget lots of stuff. I need a stock of information that I can easily search for to find where I left off.
(M1b) I'm learning so much at so many levels, I want to document this, both for myself from the future and in case there are newcomers who want to see how one newcomer did it. I'm doing it here because I don't want to clutter the actual conversations up with all of my "learner's notes".
(S1) Thanks to conversations with many in this community, I guess I can now say what "my work" is at this stage: I'm investigating whether studying category theory can help solve my most pressing problems.. At first, a few years ago, I took it on blind faith based on what experts wrote (what else could I do, since I was totally new to this!?)(now I would say I'm kind of new to this), but now it's really starting to bear fruit, and I think I can actually say something, and the least cognitively onerous place for me to put it is here, in the "community: our work" channel.
(S2) In a hat tip to @Emily Riehl , I'm studying Category Theory in Context, literally, and also, well, literally, but "up a level". I guess I could say I'm studying Category Theory in Context in Context" (Note 1). That means not only asking questions and receiving answers here about (A)CT and noticing the language that people use to talk about their ideas. Moreover, if we think about (A)CT as "the thing that (A)CTheorists do", then the higher-level context I mean is learning from the grown-ups the "right manners and good conduct" of becoming a good citizen of this community.
(S3) Pursuant to (S1) and (S2), I learned that being a good member of the (A)CT community requires knowing how to work with literal computers and the platforms that are used. That means, for example, for ACT, how to partially quote someone's message (Note 2 #TODO)!
In sum, my work is:
I'd keep my thoughts to myself, but then at least one person who teaches CT said that they appreciated my learner's stream of consciousness, so I thought it would be worth just giving it a try. Also, if even one teacher, learner, or community newcomer happens to find this and is helped by it, I think I'll feel like I will have given back to this community, which has already given me so much. (Note 4)
I'm nervous about asking questions regarding my work (my other questions were about math, so I wasn't nervous), so I'll just openly wonder whether anyone thinks it is a good idea to write about my work here.
That said, I'll just straight up ask these questions in the spirit of (S2):
I think the likeliest most harm is that, no one will read it but future me and it'll be lost and forgotten in the infinite stream of information. (Note N)
10Q4UWAA! (Note /Omega)
FAQs (Note 3)
Q: Why don't you just blog? A: A lot of reasons, but the main one is that my cognitive loading is orders of magnitude higher than it was before when I could blog, so now it's a choice between share somewhere or don't share at all.
Zoolander Q: But why APPLIED CT? A: Since the usual math examples in CT textbooks are for people who know math already (I'm only now learning area integrals at uni, and haven't taken the pure maths module yet!), I thought that I would see whether I could use some examples from my prior knowledge. Well, we might think of this as "applying category theory to learn category theory, but like, the reverse". Which, I'm pretty sure, someone can express in CT language. Maybe that can be an exercise to myself. In any case, from the perspective of context-teleporting, learning CT through my prior knowledge examples is basically "coapplying CT" and therefore, I guess, the distinction is blurred. And I only just now realized that this Zulip is actually CT Zulip! So, I can just say "CT" and everything will be okay.
NOTES
(Note 1) Here, when I say Emily's book title, it stands for all the textbooks and papers that (could this possibly what they mean by a "model category"?) I'm studying.
(Note 2) Learned from John B in the aforementioned conversation. You have to put the ``` on a NEW line! I must write about this in detail, it was very funny! Thanks, John B!
(Note 3) They're frequently asked by only me. ALL the time.
(Note 4) I'm very grateful to many people here, but I fear they're all thanked out, and I don't want to be OTT with my thanks. I'm just really grateful!
(Note N) #TODO ask this as 3rd question - but to whom? I will look in Meta:Meta for clues.
(Note \Omega) #TODO figure out how to typeset this
Spencer Breiner (Mar 18 2026 at 12:15):For latex output, put your command in double dollar signs: $$\Omega$$
David Egolf (he/him) (Mar 18 2026 at 16:08):So I'm nervous about this, but I'm going to cast a spell: sprobujemy ("let's try" in Polish) and give it a go.
Great! It can be intimidating to post here - but also really rewarding. And personally I like to take some comfort from this fact: even though my posts may have mistakes in them, they can still be of some value to others.
It is okay with everyone if I "pretendly blog" what I've learned here? ... If "community: our work" is not the place to do it, then where?
In my opinion, it's fine to start posting about category theory in whatever thread seems good to you. A moderator can move a thread (or posts within a thread), if they feel it's important! I've found #learning: questions and #learning: reading & references to be good places to post, for myself.
JR Learnstomath (Mar 20 2026 at 08:28):Spencer Breiner said:
For latex output, put your command in double dollar signs:
$$\Omega$$
Thanks, it worked on another post! I will leave this mistake and correction here #ForLearningPurposes
JR Learnstomath (Mar 20 2026 at 08:29):Really helpful signposting, 10Q ( :: my expression of gratitude), @David Egolf (he/him)
JR Learnstomath (Mar 20 2026 at 08:31):David Egolf (he/him) said:
So I'm nervous about this, but I'm going to cast a spell: sprobujemy ("let's try" in Polish) and give it a go.
...even though my posts may have mistakes in them, they can still be of some value to others.
...it's fine to start posting about category theory in whatever thread seems good to you. A moderator can move a thread (or posts within a thread), if they feel it's important! I've found #learning: questions and #learning: reading & references to be good places to post, for myself.
Really helpful tips and signposting, 10Q ( :: my expression of gratitude)!
JR Learnstomath (Mar 20 2026 at 08:40):ON SPRINGS AND THINGS
It is the first day of spring! I can already talk about one pressing problem for me: motivation. Not the intrinsic kind, but the kind where I have a hard time connecting my homework (HW) exercises to "what have I seen in my life that will get me to start studying for that exam that I feel like I desperately need to pass"?
Following @John Baez's #community: our work > John Baez 's channel, I found this gem:
"Almost any system that vibrates can be approximately modeled as a harmonic oscillator with n position and n momentum coordinates!" - John Baez, What is Entropy? 4 October 2024 @ 1:14 am.
Oh, so quoting is also an environment-type thing. The way I discovered this is that I selected all of what I wanted to quote and pressed the quotation mark button on the ribbon at the bottom. I'll repeat that same information here, but with the Zulip formatting:
Almost any system that vibrates can be approximately modeled as a harmonic oscillator with n position and n momentum coordinates! - John Baez, What is Entropy? 4 October 2024 @ 1:14 am.
In fact, even that blog title "Azimuth" has been helpful!! I had seen it a couple years ago, and I wasn't sure what it was, but in our unit on 3D surface integration stuff, I saw the word, and the diagram with the sphere and the lat/long lines, and was like -- "I know you!!!".
This is why I'm saying "studying" rather than "learning" CT, because these things aren't CT concepts in and of themselves, but they are things I discovered by following the stacked-stone-path-markers.
10Q!
JR Learnstomath (Mar 20 2026 at 08:48):Reflection
In the spirit of defining my symbols ("notation"), by ':folded_hands:', I mean "Thanks for your attention, I have read your message and I'm now thinking about it".
So that's weird, because this reminds me of when I was context-teleporting in the early 2020's, I was very unkindly spokenn to on Twitter for responding "as if I were an automated response". I was just trying to speak precisely to avoid misinterpretation :(:(:(
#ThingsThatMakeYouGo
JR Learnstomath (Mar 20 2026 at 10:30):JR Learnstomath said in #practice: industry > Category theorists in AI:
Notification Bot said:
A message was moved from this topic to #meta: off-topic > CT K-pop anthem working group by JR Learnstomath.
Woohoo it worked!! Thanks, Notification Bot!
OK it would seem that I need to figure out how to MOVE, not Forward a message to thread it to my page #TODO
JR Learnstomath (Apr 03 2026 at 11:02):UNEXPECTEDLY, CT IS HELPING ME NAVIGATE "ALL THE SQUIGGLES"
I'm hanging precariously on by my fingertips on our maths module on modeling and math methods. We're at the unit on line integrals, double integration, and the like, and my eyes are swimming because of all what a classmate called something along the lines of "all those squiggles".
Much to my surprise, reading the algebra has become a LOT easier since I've been studying CT for about 3 years now! I can kind of "see" arrows coming into an expression like f(u,v) and get less intimidated, which then helps me think.
So it's not exactly CT concepts per se -- but maybe it is. Maybe the point of CT is that it's arrows ("all the way down"?). I'll see whether I can draw what I saw in my head next time.
JR Learnstomath (Apr 14 2026 at 07:05):Just to close on this one before I dive into the submarine to try to miraculously pass this June exam, these are terrible examples of what I mean. I now see these arrows in my head, from the domain of the function to the codomain, and it's really helping a lot. These are from p. 58 and p. 86 of "Unit 16", Open University UK, MST210 Book E presentation of school year 2025/26.
Separately, studying containers is helping me with questions and answers, but I'll see whether it actually works, and talk about it this summer (either celebrating a pass, or nursing my wounds from a fail).
David Egolf (he/him) (Apr 14 2026 at 17:00):Wishing you the best for your calculus studying! The calculus sequence was not my favorite thing, despite being a fan of math in general. In the classes I took, there was a primary emphasis on being able to do certain computations. Useful, but not especially satisfying to me.
But on the bright side, I saw a lot of examples in those classes! These have been helpful to know when learning other math, which sometimes people explain using analogies to ideas from calculus.
David Egolf (he/him) (Apr 14 2026 at 17:08):More closely relating to your comments on functions, I have had at various times some difficulty with the notation used in calculus. Sometimes people will write to mean a function (instead of the value of the function at !), which I found confusing - especially in the context of differentiation.
David Egolf (he/him) (Apr 14 2026 at 17:22):For example, in algebra we might be presented with something like and be told to solve. In this case, we are looking for the numbers we can plug in for that square to 1.
But in calculus, we might be presented with and be asked to do things involving derivatives, especially in the context of "implicit differentiation". For taking derivatives here to make sense, we must be talking about functions. So now we must interpret and somehow in terms of functions!