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- W4384826091 abstract "Abstract In this paper we show that a finite product preserving opfibration can be factorized through an opfibration with the same property, but with groupoidal fibres. If moreover the codomain is additive, one can endow each fibre of the new opfibration with a canonical symmetric 2-group structure. We then apply such factorization to the opfibration that sends a crossed extension of a group C to its corresponding C -module. The symmetric 2-group structure so obtained on the fibres, defines the third cohomology 2-group of C , with coefficients in a C -module. We show that the usual third and second cohomology groups are recovered as its homotopy invariants. Furthermore, even if all results are presented in the category of groups, their proofs are valid in any strongly protomodular semi-abelian category, once one adopts the corresponding internal notions." @default.
- W4384826091 created "2023-07-21" @default.
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- W4384826091 date "2023-07-19" @default.
- W4384826091 modified "2023-10-17" @default.
- W4384826091 title "The Third Cohomology 2-Group" @default.
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- W4384826091 doi "https://doi.org/10.1007/s00032-023-00383-4" @default.
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