# Semisimplicial spaces

@article{Ebert2019SemisimplicialS,
title={Semisimplicial spaces},
author={Johannes Ebert and Oscar Randal-Williams},
journal={Algebraic \& Geometric Topology},
year={2019}
}
• Published 10 May 2017
• Mathematics
• Algebraic & Geometric Topology
This is an exposition of homotopical results on the geometric realization of semisimplicial spaces. We then use these to derive basic foundational results about classifying spaces of topological categories, possibly without units. The topics considered include: fibrancy conditions on topological categories; the effect on classifying spaces of freely adjoining units; approximate notions of units; Quillen’s Theorems A and B for non-unital topological categories; the effect on classifying spaces…
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