Homology of n-fold groupoids

Tomas Everaert and Marino Gran

Any semi-abelian category A appears, via the discrete functor, as a full replete reflective subcategory of the semi-abelian category of internal groupoids in A. This allows one to study the homology of $n$-fold internal groupoids with coefficients in a semi-abelian category A, and to compute explicit higher Hopf formulae. The crucial concept making such computations possible is the notion of protoadditive functor, which can be seen as a natural generalisation of the notion of additive functor.

Keywords: Protoadditive functor, categorical Galois theory, internal groupoid, semi-abelian category, homology, Hopf formula

2000 MSC: 8G, 20J, 55N35, 18E10, 20L

Theory and Applications of Categories, Vol. 23, 2010, No. 2, pp 22-41.


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