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arXiv 0905.3884math.CTmath.RA
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Gabriel Galois覆盖函子II的推广：2-范畴Cohen-Montgomery对偶

A generalization of Gabriel's Galois covering functors II: 2-categorical Cohen-Montgomery duality

Hideto Asashiba

备注：
31 pages. I moved the Sec of G-GrCat into Sec 3, and added Lem 5.6. I added more explanations in the proof of Cor 7.6 with (7.5). I added Def 7.7 and Lem 7.8 with the necessary additional assumptions in Props 7.9 and 7.11. I added Lem 8.8 with a short proof, Rmk 8.9 and the proof of Lem 8.10. The final publication is available at Springer via http://dx.doi.org/10.1007/s10485-015-9416-9
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摘要：

给定一个群$G$，我们在所有具有$G$ -作用的小范畴类和所有小$G$ -分次范畴类上定义了合适的2-范畴结构，并证明了轨道范畴构造的2-范畴扩张和Smash积构造的2-范畴扩张是2-等价的（相互2-拟逆），从而推广了Cohen-Montgomery对偶.

英文摘要：

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.

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