Derived equivalences of actions of a category

Details Derived equivalences of actions of a category Derived equivalences of actions of a category

2011-11-09

arxiv.org/abs/1111.2239v2

Mathematics

Representation Theory

23 pages, ver 2: A construction of oplax functors using a comonad is added by generalizing a tiny example that should be corre

Scientific paper

Let $\Bbbk$ be a commutative ring and $I$ a category. As a generalization of a $\Bbbk$-category with a (pseudo) action of a group we consider a family of $\Bbbk$-categories with a (pseudo, lax, or oplax) action of $I$, namely an oplax functor from $I$ to the 2-category of small $\Bbbk$-categories. We investigate derived equivalences of those oplax functors, and establish a Morita type theorem for them. This gives a base of investigations of derived equivalences of Grothendieck constructions of those oplax functors.

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