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visits member for 2 years, 10 months
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Aug
17
comment Identities that connect antipode with multiplication and comultiplication
This is what I need, thank you!
Aug
17
accepted Identities that connect antipode with multiplication and comultiplication
Aug
13
comment Is the ideal of functions vanishing at a set complementable in $C(X)$?
@NarutakaOZAWA, could you, please, give the reference?
Aug
13
comment Is the ideal of functions vanishing at a set complementable in $C(X)$?
Yes, that's unexpected. Thank you, Bill.
Aug
13
accepted Is the ideal of functions vanishing at a set complementable in $C(X)$?
Aug
13
comment Is the ideal of functions vanishing at a set complementable in $C(X)$?
Yes, excuse me and thank you!
Aug
12
comment Is the ideal of functions vanishing at a set complementable in $C(X)$?
But $\beta{\mathbb N}\setminus{\mathbb N}$ is not closed in $\beta{\mathbb N}$.
Aug
12
asked Is the ideal of functions vanishing at a set complementable in $C(X)$?
Aug
12
revised Identities that connect antipode with multiplication and comultiplication
added 35 characters in body
Aug
12
comment Identities that connect antipode with multiplication and comultiplication
As far as I understand, Sweedler considers Hopf algebras in the category of vector spaces. Is the same true for all (braded?) monoidal categories?
Aug
12
revised Identities that connect antipode with multiplication and comultiplication
deleted 3 characters in body
Aug
12
asked Identities that connect antipode with multiplication and comultiplication
Aug
5
accepted Is antipode unique for bialgebras in arbitrary monoidal categories?
Aug
5
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
They are visual, that's important. It will take me some time to look at the explanations. Thank you, Darij!
Aug
5
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
Yes, I expected something like this from the very beginning. But, Darij, it's not correct to write $f\otimes g\otimes h$. You should write either $(f\otimes g)\otimes h$ or $f\otimes (g\otimes h)$, and this is a supplementary headache here. If you don't mind, I think, I'll accept the answer by Evan after getting accustomed to his style. :)
Aug
5
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
I did not see such a proof. Do you mean this trick with string diagrams?
Aug
5
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
@darij grinberg: This becomes obvious only if the assocoativity of convolution in $Hom(B^c,B^a)$ is already proved. This fact is not obvious -- in the book by Dascalescu, Nastasescu and Raianu, for example, they use the Sweedler notations for proving it. But the Sweedler notations, I would say, is a risky way in arbitrary monoidal categories. Chari and Pressley mention this fact, but without references. These were two sources for me. I saw before the pictures like those that Evan Jenkins gave in his answer, but I did not understand them and I did not know that they can be used here.
Aug
5
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
Dima, thank you!
Aug
5
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
Todd and UwF, thank you!
Aug
4
comment Is antipode unique for bialgebras in arbitrary monoidal categories?
@UwF: I guessed also. :) But this style of explanation - "I drop a hint, you guess!" - is a bit annoying when you need a reference for a paper. Are there texts where this technique is described more or less intelligible? :)