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arXiv · 1705.03774

Semi-simplicial spaces

Johannes Ebert·Oscar Randal-Williams
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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.

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BibTeXRIS

Johannes Ebert, Oscar Randal-Williams. 2017-05-10. Semi-simplicial spaces. https://doi.org/10.2140/agt.2019.19.2099

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