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2019 Semisimplicial spaces
Johannes Ebert, Oscar Randal-Williams
Algebr. Geom. Topol. 19(4): 2099-2150 (2019). DOI: 10.2140/agt.2019.19.2099

Abstract

This is an exposition of homotopical results on the geometric realisation 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 nonunital topological categories; the effect on classifying spaces of changing the topology on the space of objects; the group-completion theorem.

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Johannes Ebert. Oscar Randal-Williams. "Semisimplicial spaces." Algebr. Geom. Topol. 19 (4) 2099 - 2150, 2019. https://doi.org/10.2140/agt.2019.19.2099

Information

Received: 29 August 2018; Revised: 20 December 2018; Accepted: 3 January 2019; Published: 2019
First available in Project Euclid: 22 August 2019

zbMATH: 07121522
MathSciNet: MR3995026
Digital Object Identifier: 10.2140/agt.2019.19.2099

Subjects:
Primary: 18G30, 55R35, 55U10

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 4 • 2019
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