On Gr-functors between Gr-categories
نویسنده
چکیده
Each Gr-category (or categorical group) is Gr-equivalent to a Grcategory of type (Π, A, ξ), where Π is a group, A is a Π-module and ξ is a 3-cocycle of Π, with coefficients in A. In this paper, first we show that each Gr-functor induces one between Gr-categories of type (Π, C). Then we give results on the existence of Gr-functor and the classification of Gr-functors by cohomology groups H(Π, C), H(Π, C).
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ON GR-FUNCTORS BETWEEN GR-CATEGORIES: OBSTRUCTION THEORY FOR GR-FUNCTORS OF THE TYPE (φ, f)
Each Gr-functor of the type (φ, f) of a Gr-category of the type (Π, C) has the obstruction be an element k ∈ H(Π, C). When this obstruction vanishes, there exists a bijection between congruence classes of Gr-functors of the type (φ, f) and the cohomology group H(Π,C). Then the relation of Gr-category theory and the group extension problem can be established and used to prove that each Gr-catego...
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