The first cohomology object in semi-abelian categories
 
 
Description:  We show that there is a natural notion of internal crossed homomorphism object of a split extension, defined as the representing object of a certain functor. Using these objects one can construct the first internal cohomology object of a split extension. We show that although these objects can be defined for an arbitrary split extension, they depend only on the center of the split extension. We show under suitable conditions that for abelian split extensions these internal cohomology objects coincide with those introduced in the author's PhD thesis.
Date:  2021-06-15
Start Time:   15:00
Speaker:  James Gray (Stellenbosch Univ., South Africa)
Institution:  Stellenbosch University
Place:  Zoom
Research Groups: -Algebra, Logic and Topology
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