2
votes
0answers
149 views

(Non trivial) coidempotents(Co-$K$-theory)

I was interested to know about coalgebraic version of "Idempotents". So I seached the web and I found the following interesting post : ...
5
votes
2answers
254 views

Free cocommutative commutative Hopf monoids

I have some questions about generalizations of abelian groups, relative to symmetric monoidal categories. 1) Let $C$ be a cocomplete cartesian monoidal category with equalizers. I can show that the ...
3
votes
3answers
1k views

Mistake in Wikipedia Entry “Coalgebra”

Consider the following quote from the Wikipedia entry Coalgebra: The kernel of every coalgebra morphism $f : C_1 \to C_2$ is a coideal in $C_1$, and the image is a subcoalgebra of $C_2$. I can't ...
5
votes
2answers
441 views

Primitive elements of a tensor product of bialgebras

Given a field $k$ of characteristic $0$. For every $k$-bialgebra $A$, let $\mathrm{Prim} A$ denote the $k$-vector subspace of $A$ consisting of all primitive elements of $A$. What conditions can we ...
8
votes
1answer
660 views

Connected graded involutive bialgebras (Hopf algebras) sought (for Dynkin idempotent checking)

Again, there is a general and a concrete question: Concrete question. Let $H$ be a connected graded bialgebra over a commutative ring $k$ with unity (where graded means $\mathbb N$-graded). Then, it ...
1
vote
1answer
136 views

Linear functional kills all primitives of a connected filtered coalgebra => it lies in m^2?

Let $C$ be a connected filtered coalgebra over a field $k$. Maybe $k$ has characteristic $0$ (though I don't know where this can be of use). Let $1$ denote the unique element of $C_0$ mapping to $1\in ...
4
votes
1answer
345 views

Coderivations of S(V) correspond to linear maps S(V) -> V. Only over characteristic 0?

Definition. Let $k$ be a commutative ring. Let $V$ be a $k$-module. We turn the symmetric algebra $\mathrm{S}\left(V\right)$ of $V$ into a graded Hopf algebra by defining the comultiplication $\Delta ...
6
votes
1answer
528 views

Distributions on product spaces

I hope this is suitable to MO. Question. Let $X$ and $Y$ be two open sets in $\mathbb R^n$ and $\mathbb R^m$, respectively. In what sense can we consider $\mathcal{D}^{\prime} \left(X\times Y\right)$ ...
5
votes
1answer
730 views

What kind of structures allow Galois descent?

EDIT: Question solved. Let me explain what I mean. The classical formulation of Galois descent, e. g. in Crawley-Boevey's "Cohomology and central simple algebras", uses the following notion: ...
0
votes
1answer
327 views

How is the coradical filtration defined?

I have seen the coradical filtration of a coalgebra $C$ defined as follows: $C_0 = \text{sum of all simple subcoalgebras of }C$; for any $n\geq 1$, let $C_n$ be $\Delta^{-1}\left(C\otimes ...