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

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.

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

References in corpus (2)

• On triangulated orbit categories
• On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles

Cited by in corpus (4)

• The Grothendieck Construction and Gradings for Enriched Categories
• Auslander Correspondence for Triangulated Categories
• A generalization of Gabriel's Galois covering functors and derived equivalences
• The dual actions, equivariant autoequivalences and stable tilting objects