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.
http://www.tac.mta.ca/tac/volumes/23/2/23-02.dvi
http://www.tac.mta.ca/tac/volumes/23/2/23-02.ps
http://www.tac.mta.ca/tac/volumes/23/2/23-02.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/2/23-02.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/23/2/23-02.ps