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SUMMARY:Higher categorical foundations of Giraud's non-abelian cohomology 
 - Alexander Campbell (Macquarie University)
DTSTART:20150811T131500Z
DTEND:20150811T141500Z
UID:TALK60200@talks.cam.ac.uk
CONTACT:Zhen Lin Low
DESCRIPTION:The aim of this talk is to expose the natural foundations of n
 on-abelian cohomology within higher category theory\, as expounded by Grot
 hendieck and Street among others. The fundamental principle is that higher
  stacks are the natural coefficients for non-abelian cohomology\; the coho
 mology is the higher category of global sections of the higher stack. The 
 familiar definitions of non-abelian cohomology of degree one and two in te
 rms of torsors and gerbes are recovered by using a generalisation of Lawve
 re's construction of the associated sheaf of a presheaf. \n\nI will compar
 e this theory with that presented in Street's paper 'Categorical and combi
 natorial aspects of descent theory'\, and address the "future quest" propo
 sed in the last sentence of that paper. I will also outline a method for d
 eveloping the required category theory of bicategories and tricategories v
 ia the homotopy coherent category theory of model 2-categories and model G
 ray-categories.
LOCATION:MR5\, Centre for Mathematical Sciences
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