Geodesic
Crossed modules and symmetric cohomology of groups
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 123-134.

Voir la notice de l'article provenant de la source International Press of Boston

This paper links the third symmetric cohomology (introduced by Staic [10] and Zarelua [12]) to crossed modules with certain properties. The equivalent result in the language of $2$‑groups states that an extension of $2$-groups corresponds to an element of $HS^3$ iff it possesses a section which preserves inverses in the $2$‑categorical sense. This ties in with Staic’s (and Zarelua’s) result regarding $HS^2$ and abelian extensions of groups.
DOI : 10.4310/HHA.2020.v22.n2.a7
Classification : 18D05, 20J06
Keywords: group cohomology, crossed modules, symmetric cohomology 
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     title = {Crossed modules and symmetric cohomology of groups},
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Mariam Pirashvili. Crossed modules and symmetric cohomology of groups. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 123-134. doi : 10.4310/HHA.2020.v22.n2.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a7/

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