A Generalization of Gabriel's Galois Covering Functors II: 2-Categorical Cohen-Montgomery Duality

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. Further we characterize equivalences in both 2-categories.