The cohomological comparison arising from the associated abelian object

Publication date: 6 January 2010

Abstract: We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at the level of the slice category D/Y, are actually isomorphisms. These conditions hold in particular when D is the category Gp of groups, and this allows us to give a new insight on the Eilenberg-Mac Lane cohomology of groups. They hold also when D is the category K-Lie of Lie-algebras.

This page was built for publication: The cohomological comparison arising from the associated abelian object

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6216970)