Abstract
Throughout this article, we fix a group G and a commutative ring $$\Bbbk $$ . This is an exposition on 2-equivalences between a 2-category of small $$\Bbbk $$ -categories with pseudo G-actions and a 2-category of G-graded small $$\Bbbk $$ -categories, which generalizes (Asashiba in Appl Categor Sturct 25(8):3278–3296, 2017). This article is a translation of some parts of Ch. 4 and 5 in the book (Asashiba in Categories and representation theory, focused on 2-categorical covering theory, SGC library 155, Saiensu-sha, 2019) in Japanese.
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