Cohen–Montgomery Duality for Pseudo-actions of a Group

Throughout this article we fix a group G and a commutative ring k . This is an exposition on 2-equivalences between a 2-category of small k -categories with pseudo G -actions and a 2-category of G -graded small k -categories, which generalizes [5]. This article is a translation of some parts of Ch. 4 and 5 in the book [10] in Japanese.