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Derived Equivalences of Actions of a Category

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Hideto Asashiba

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  1. Hideto Asashiba
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Correspondence to Hideto Asashiba.

Additional information

This work is partially supported by Grant-in-Aid for Scientific Research (C) 21540036 from JSPS.

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Asashiba, H. Derived Equivalences of Actions of a Category. Appl Categor Struct 21, 811–836 (2013). https://doi.org/10.1007/s10485-012-9284-5

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  • DOI: https://doi.org/10.1007/s10485-012-9284-5

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