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arXiv · 1906.01011

An algebraic representation of globular sets

A. M. Medina-Mardones
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Abstract

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 \mbox{$R$-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.

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A. M. Medina-Mardones. 2019-06-03. An algebraic representation of globular sets. https://arxiv.org/abs/1906.01011

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