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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
vote
Accepted
How to make commutative algebraic groups strongly dualizable?
Since Ilya asked I'll write out in a bit more detail the case of finitely generated abelian groups. There is not (as far as I know) any reasonable notion of strong duality on the abelian category of f …
2
votes
Morita equivalence and moduli problems
This is not an example of the kind you asked for, but you might find this interesting anyway - it does involve both moduli and equivalences. In Bridgeland's paper Flops and Derived Categories he const …
5
votes
When does "splits" imply "cosplits"?
So the fact that you had a hard time thinking of cosplit sequences of groups and the last question got me thinking (along the lines of Joel's comment actually)... what I came up with is probably stand …
3
votes
Applications of classifying thick subcategories
I'm not completely sure if this is the sort of thing you are after, but the telescope conjecture (conjecture isn't a great word as it is known to be false for some categories) springs to mind as somet …