Derived equivalences of actions of a category
Abstract
Let be a commutative ring and a category. As a generalization of a -category with a (pseudo) action of a group we consider a family of -categories with a (pseudo, lax, or oplax) action of , namely an oplax functor from to the 2-category of small -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.
Cite
@article{arxiv.1111.2239,
title = {Derived equivalences of actions of a category},
author = {Hideto Asashiba},
journal= {arXiv preprint arXiv:1111.2239},
year = {2012}
}
Comments
23 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 relation\beta'\alpha'= \id_{x'} on X(2) or changing the definition of X(a) to "X(a)(z):= y' for z=x,y and X(a)(\gamma):= \id_{y'} for \gamma = \id_x, \id_y, \alpha, \beta" in Section 2. Some references were added