Geodesic
Twisted simplicial groups and twisted homology of categories
Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 111-130.

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

Let $A$ be either a simplicial complex $K$ or a small category $\mathcal{C}$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function\[\delta \colon V(A) \longrightarrow \mathrm{End}(G), \quad v\mapsto \delta_v,\]such that $\delta_v \circ \delta_w = \delta_w \circ \delta_v$ if there exists an edge in $A$ joining $v$ with $w$ or an arrow either from $v$ to $w$ or from $w$ to $v$. We give a canonical construction of twisted simplicial groups as well as twisted homology for $A$ with a given twisted structure. Also we determine the homotopy type of this simplicial group as the loop space over certain twisted smash product.
DOI : 10.4310/HHA.2017.v19.n2.a7
Classification : 55U10, 18G30
Keywords: homology, simplicial group, category 
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     title = {Twisted simplicial groups and twisted homology of categories},
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J. Y. Li; V. V. Vershinin; J. Wu. Twisted simplicial groups and twisted homology of categories. Homology, homotopy, and applications, Tome 19 (2017) no. 2, pp. 111-130. doi : 10.4310/HHA.2017.v19.n2.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2017.v19.n2.a7/

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