Derived equivalences of actions of a category

Abstract

Let $\mathbb{k}$ be a commutative ring and $I$ a category. As a generalization of a $\mathbb{k}$-category with a (pseudo) action of a group we consider a family of $\mathbb{k}$-categories with a (pseudo, lax, or oplax) action of $I$, namely an oplax functor from $I$ to the 2-category of small $\mathbb{k}$-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.

arXiv comment23 pages, ver 2: A construction of oplax functors using a comonad is added by generalizing a tiny example that should be corrected either by putting a relationβ'α'= \id_{x'} on X(2) or changing the definition of X(a) to "X(a)(z):= y' for z=x,y and X(a)(γ):= \id_{y'} for γ= \id_x, \id_y, α, β" in Section 2. Some references were added

References in corpus (1)

• The Grothendieck Construction and Gradings for Enriched Categories

Cited by in corpus (1)

• Presentations of Grothendieck constructions