An algebraic representation of globular sets
Algebraic Topology
2019-08-14 v2 Category Theory
Abstract
We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric -coalgebras when is an integral domain. This embedding is a lift of the usual functor of -chains and the extra structure consists of a derived form of cup coproduct. Additionally, we construct a functor from group-like counital cosymmetric \mbox{-coalgebras} to -categories and use it to connect two fundamental constructions associated to oriented simplices: Steenrod's cup- coproducts and Street's orientals. The first defines the square operations in the cohomology of spaces, the second, the nerve of higher-dimensional categories.
Cite
@article{arxiv.1906.01011,
title = {An algebraic representation of globular sets},
author = {A. M. Medina-Mardones},
journal= {arXiv preprint arXiv:1906.01011},
year = {2019}
}