Semi-simplicial spaces

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.

32 pages; v2: Simplified proof of the Group-Completion Theorem

References in corpus (1)

• Homological stability for moduli spaces of high dimensional manifolds

Cited by in corpus (17)

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• Homological stability for moduli spaces of disconnected submanifolds, I
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