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**1 - 4**of**4**### A COMPARISON THEOREM FOR SIMPLICIAL RESOLUTIONS

- JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, VOL. 2(1), 2007, PP.109–126
, 2007

"... It is well known that Barr and Beck’s definition of comonadic homology makes sense also with a functor of coefficients taking values in a semi-abelian category instead of an abelian one. The question arises whether such a homology theory has the same convenient properties as in the abelian case. Her ..."

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It is well known that Barr and Beck’s definition of comonadic homology makes sense also with a functor of coefficients taking values in a semi-abelian category instead of an abelian one. The question arises whether such a homology theory has the same convenient properties as in the abelian case. Here we focus on independence of the chosen comonad: conditions for homology to depend on the induced class of projectives only.

### A “WORKING MATHEMATICIAN’S ” DEFINITION OF SEMI-ABELIAN CATEGORIES

"... Abstract. Semi-abelian and finitely cocomplete homological categories are character-ized in terms of four resp. three simple axioms, in terms of the basic categorical notions introduced in the first few chapters of MacLane’s classical book. As an immediate ap-plication we show that categories of dia ..."

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Abstract. Semi-abelian and finitely cocomplete homological categories are character-ized in terms of four resp. three simple axioms, in terms of the basic categorical notions introduced in the first few chapters of MacLane’s classical book. As an immediate ap-plication we show that categories of diagrams in semi-abelian and similar categories are