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Results tagged with coalgebras
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user 290
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
32
votes
What is a coalgebra intuitively?
Coalgebras appear naturally in combinatorics as describing ways one can decompose objects into other objects of the same type. … I learned this point of view from Gian-Carlo Rota's Coalgebras and bialgebras in combinatorics, which I currently cannot find an online copy of... …
3
votes
(Co)Universal Property of Quotients/Subs
1) The answer appears to be no; this was discussed on MO previously.
2) The symmetric algebra functor is left adjoint to the forgetful functor from commutative algebras to vector spaces (over a fiel …
- 118k
3
votes
Accepted
Why the preimage rather than image in Stone-type dualities.
You should think of the preimage as taking the pullback of $\mathbb{F}_2$-valued functions. For any topological space $X$, the space of continuous functions $X \to \mathbb{F}_2$ may be identified with …
- 118k
7
votes
Accepted
Comultiplication on objects in an (abelian?) category
Sure, we can define such things. Let's work in the Morita 2-category $\text{Mor}(k)$ over a commutative ring $k$, which has
objects $k$-algebras $A$,
morphisms $k$-bimodules (with composition given …
- 118k