On a simplicial monoid whose underlying simplicial set is not a quasi-category
Category Theory
2020-06-23 v2 Algebraic Topology
Combinatorics
Abstract
It is well known that the underlying simplicial set of any simplicial group is a Kan complex. Roughly speaking, Kan complex is an infinite-dimensional analogue of groupoid, and the relation between groupoids and categories resembles that between groups and monoids. Thus one may ask if the underlying simplicial set of each simplicial monoid is a quasi-category. In this short note, we construct a simplicial monoid whose underlying simplicial set is not a quasi-category.
Keywords
Cite
@article{arxiv.2006.01403,
title = {On a simplicial monoid whose underlying simplicial set is not a quasi-category},
author = {Ryo Horiuchi},
journal= {arXiv preprint arXiv:2006.01403},
year = {2020}
}
Comments
Fixed typos