Resolutions, higher extensions and the relative Mal'tsev axiom
 
 
Description:  We study how the concept of higher-dimensional extension which comes from categorical Galois theory relates to simplicial resolutions and homology. For instance, an augmented simplicial object is a resolution if and only if its truncation in every dimension gives a higher extension, in which sense resolutions are infinite-dimensional extensions or higher extensions are finite-dimensional resolutions. We also relate certain stability conditions of extensions to the Kan property for simplicial objects. This gives rise to a notion of relative Mal'tsev category, which is weaker than Tamar Janelidze's relative homological categories and which reduces to the Mal'tsev condition in the case of regular epimorphisms in a regular category. In this context we prove a relative version of the result that a regular category is Mal'tsev if and only if every simplicial object in the category is Kan. We then use this result (and our entire setting) to define homology of an object with coefficients in a relative semi-abelian category.
(Joint work with Tomas Everaert and Julia Goedecke)
Date:  2010-09-14
Start Time:   14:30
Speaker:  Tim Van der Linden (CMUC)
Institution:  CMUC
Place:  Sala 5.5
Research Groups: -Algebra, Logic and Topology
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