Título: COHOMOLOGY OF CROSSED MODULES

Palestrante: GURAM DONADZE (Institute of Cybernetics of Georgian Technical University, Tbilisi, Georgia)

 

Abstract:

Crossed modules were introduced by Whitehead [7]. They are algebraic models of 2-homotopy types [1]. There are two different approaches to (co)homology of crossed modules. The first one is via the classifying spaces of crossed modules [1], [3], [5].
The second one is purely algebraic and is based on cotriple cohomology [2]. These approaches are not equivalent but are connected via an exact sequence constructed

in [6]. In [4] Pirashvili gave  "cocycle" description of low dimensional cotriple co-homology with arbitrary coefficients. I am going to talk on the results obtained
in [4].