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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.
Keywords: semisimplicial space, geometric realisation, Quillen Theorem A, Quillen Theorem B, group-completion
Ebert, Johannes 1 ; Randal-Williams, Oscar 2
@article{10_2140_agt_2019_19_2099,
author = {Ebert, Johannes and Randal-Williams, Oscar},
title = {Semisimplicial spaces},
journal = {Algebraic and Geometric Topology},
pages = {2099--2150},
publisher = {mathdoc},
volume = {19},
number = {4},
year = {2019},
doi = {10.2140/agt.2019.19.2099},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2099/}
}
TY - JOUR AU - Ebert, Johannes AU - Randal-Williams, Oscar TI - Semisimplicial spaces JO - Algebraic and Geometric Topology PY - 2019 SP - 2099 EP - 2150 VL - 19 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.2099/ DO - 10.2140/agt.2019.19.2099 ID - 10_2140_agt_2019_19_2099 ER -
Ebert, Johannes; Randal-Williams, Oscar. Semisimplicial spaces. Algebraic and Geometric Topology, Tome 19 (2019) no. 4, pp. 2099-2150. doi: 10.2140/agt.2019.19.2099
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