The cohomological comparison arising from the associated abelian object - Mathematics > Category TheoryReport as inadecuate




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Abstract: We make explicit some conditions on a semi-abelian category D such that, forany abelian group A in D and any object Y in D, the cohomology grouphomomorphisms with coefficients in A, induced by the inclusion of the abelianobjects 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, andthis allows us to give a new insight on the Eilenberg-Mac Lane cohomology ofgroups. They hold also when D is the category K-Lie of Lie-algebras.



Author: Dominique Bourn

Source: https://arxiv.org/



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