Abstract
The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in Mesablishvili (Trans. A. Razmadze Math. Inst. 173(2), 137–155, 2019). We show that descent cohomology includes Serre’s non-abelian group cohomology as a special case. This enables us to generalize Serre’s theory further to include monoids.
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