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4
votes
1answer
87 views

Comodule analogue for statement that a faithful representation of an affine group scheme generates all

If $V$ is a faithful finite dimensional representation of an affine group scheme $G$ over a field $k$, then every finite dimensional representation of $G$ is isomorphic to a subquotient of $\otimes^n ...
1
vote
0answers
97 views

Intuitive idea: What is the motivation for relative homological algebra

Basically I was wondering what is the purpous of choosing a smaller class of epis in a category? Does it allow for the existence of "more" "projective-like" objects? What are some applications? For ...
2
votes
0answers
49 views

modules and comodules related to BP_*

Let BP be the Brown Peterson spectrum. We know that the category of $BP_* BP$-comodules is an abelian category. Consider the category of $BP_* BP$-comodules, which are finitely presented as ...
2
votes
1answer
163 views

Changing Left Comodules into Right Comodules via the Antipode, and Comodule Tensor Products

Let $H$ be a Hopf algebra, with invertible antipode, and let $(M,\Delta_M)$ and $(N,\Delta_N)$ be two left $H$-comodules. Now as we all know, we have a left $H$-comodule structure on the tensor ...