University of Cambridge > Talks.cam > Extraordinary Category Theory Seminar > Higher categorical foundations of Giraud's non-abelian cohomology

Higher categorical foundations of Giraud's non-abelian cohomology

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Zhen Lin Low.

The aim of this talk is to expose the natural foundations of non-abelian cohomology within higher category theory, as expounded by Grothendieck and Street among others. The fundamental principle is that higher stacks are the natural coefficients for non-abelian cohomology; the cohomology is the higher category of global sections of the higher stack. The familiar definitions of non-abelian cohomology of degree one and two in terms of torsors and gerbes are recovered by using a generalisation of Lawvere’s construction of the associated sheaf of a presheaf.

I will compare this theory with that presented in Street’s paper ‘Categorical and combinatorial aspects of descent theory’, and address the “future quest” proposed in the last sentence of that paper. I will also outline a method for developing the required category theory of bicategories and tricategories via the homotopy coherent category theory of model 2-categories and model Gray-categories.

This talk is part of the Extraordinary Category Theory Seminar series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2024 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity