Abstract
Given a group G, we define suitable 2-categorical structures on the class of all small categories with G-actions and on the class of all small G-graded categories, and prove that 2-categorical extensions of the orbit category construction and of the smash product construction turn out to be 2-equivalences (2-quasi-inverses to each other), which extends the Cohen-Montgomery duality. Further we characterize equivalences in both 2-categories.
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This work is partially supported by Grant-in-Aid for Scientific Research (C) 21540036 and Challenging Exploratory Research 25610003 from JSPS
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Asashiba, H. A Generalization of Gabriel’s Galois Covering Functors II: 2-Categorical Cohen-Montgomery Duality. Appl Categor Struct 25, 155–186 (2017). https://doi.org/10.1007/s10485-015-9416-9
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DOI: https://doi.org/10.1007/s10485-015-9416-9