Abstract
We describe cohomologically trivial internal categories in the categoryC of groups with operations satisfying certain conditions ([15], [16]). As particular cases we obtain: ifC=Gr, H0(C, −)=0 iff C is a connected internal category; ifC=Ab,H 1(C, −)=0 iff C is equivalent to the discrete internal category (Cokerd, Cokerd, 1, 1, 1, 1). We also discuss related questions concerning extensions, internal categories, their cohomology and equivalence in the categoryC.
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Datuashvili, T. Cohomologically trivial internal categories in categories of groups with operations. Appl Categor Struct 3, 221–237 (1995). https://doi.org/10.1007/BF00878442
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DOI: https://doi.org/10.1007/BF00878442