@Yilmaz It follows from "level exchange," where you can pull morphisms past each other by composing with the identity, similar to your other question.

@Yilmaz You might need to scroll to see the whole line. I did forget the middle id, thanks! Fixed now.

The Russian sample looks very nice and is much more legible than the usual, which I guess is Computer Modern or some variant.

@Hajime_Saito Look up "rigid monoidal category." Bugs is giving a shorthand for an evaluation map α, a coevaluation map β, and dual objects X and Y. Monoidal functors preserve duality.

@GerryMyerson It's a repetitive redundancy.

This really is not an "opinion-based" question, although it might be borderline "research-level." But isn't the standard here supposed to be analogous to a colleague wandering into your office to ask something? I'll bet a lot of colleagues have had similar questions about why algebraic geometry is so heavy on category theory.

"Faithful" also has a related meaning like "accurate" or "without distortion," as in "faithful translation," which I think is similar to точный.

Well, I thought it was useful and upvoted the question and the answer.

This absolutely is the correct answer and maybe some OG German mathematicians would weigh in here. As for the complaints that it's obsolete, well, Fraktur is "obsolete" as a printed font also. Sütterlinschrift is the corresponding handwritten version. It's not that hard to remember (or distinguish) the half-dozen or so letters that are acutally used in Lie theory.

The circles of Apollonius one is nice. Much better than the usual "math art."

@Brodda Probably the same timezone where it's AD 2013

@PaulTaylor What's an intellectually structured subject?

Referring to yourself in the third person puts you in a lot of bad company.

The problem is that coming up with a mathematical proof is not at all like software engineering, and writing the proof is not nearly so enjoyable for a lot of people. It's kind of like suggesting that an aspiring poet become a copyeditor instead.