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Semisimplicial spaces

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Ebert, J 
Randal-Williams, Oscar  ORCID logo  https://orcid.org/0000-0002-7479-2878

Abstract

This is an exposition of homotopical results on the geometric realization of semi-simplicial 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 of changing the topology on the space of objects; the Group-Completion Theorem.

Description

Keywords

math.AT, math.AT, 18G30, 55U10, 55R35

Journal Title

Algebraic and Geometric Topology

Conference Name

Journal ISSN

1472-2747
1472-2739

Volume Title

19

Publisher

Mathematical Sciences Publishers
Sponsorship
Engineering and Physical Sciences Research Council (EP/M027783/1)
J. Ebert was partially supported by the SFB 878. O. Randal-Williams was supported by EPSRC grant number EP/M027783/1.