engleski

2-categorical descent, monoidal actions and Hopf algebras

In Tannakian philosophy, roughly speaking, Hopf algebras are interchangeable with their categories of modules. Similarly when globalizing actions of Hopf algebras to nonaffine situations, describing the situation in terms of categorical actions is unavoidable. I will describe several examples where this point of view is very fruitful, leading to appropriate versions of actions on noncommutative projective varieties, including quantum flag variaties, corresponding equivariant sheaves, giving a framework for natural appearance of distributive laws like entwining structures and more general ones. This is also the framework in which some related notions, like lax versions of descent may be treated. Duskin has considered 2-categorical descent in 1980-s. Ordinary descent data in Galois descent along torsors correspond to equivariant sheaves. I developed a 2-categorical analogue of equivariant objects with aim to develop a 2-Galois theory yielding an 2-equivalence between the 2-category of equivariant sheaves on torsor of a categorical group and the 2-category of ordinary sheaves on the base.

descent theory; Hopf modules; monoidal categories; distributive laws; equivariant objects; 2-categories

nije evidentirano