bio | website | mathnet.ru/php/… |
---|---|---|
location | ||
age | ||
visits | member for | 3 years, 5 months |
seen | 2 hours ago | |
stats | profile views | 1,571 |
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? :) |
Aug 4 |
comment |
Is antipode unique for bialgebras in arbitrary monoidal categories?
Yes, I guessed. However, a text with explanations would be highly appreciated. |
Aug 4 |
comment |
Is antipode unique for bialgebras in arbitrary monoidal categories?
Evan, I don't understand these pictures. Do you know a text where they are explained? |
Aug 4 |
revised |
Is antipode unique for bialgebras in arbitrary monoidal categories?
added 3 characters in body |