Geodesic
An algebraic representation of globular sets
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 135-150.

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

We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift of the usual functor of $R$-chains and the extra structure consists of a derived form of cup coproduct. Additionally, we construct a functor from group-like counital cosymmetric $R$-coalgebras to $\omega$-categories and use it to connect two fundamental constructions associated to oriented simplices: Steenrod’s cup‑$i$ coproducts and Street’s orientals. The first defines the square operations in the cohomology of spaces, the second, the nerve of higher-dimensional categories.
DOI : 10.4310/HHA.2020.v22.n2.a8
Classification : 18D05, 55S05
Keywords: globular sets, higher categories, $E_{\infty}$-structures, Steenrod cup‑$i$ products 
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     title = {An algebraic representation of globular sets},
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Anibal M. Medina-Mardones. An algebraic representation of globular sets. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 135-150. doi : 10.4310/HHA.2020.v22.n2.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a8/

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