Semisimplicial spaces

By Johannes Ebert, O. Randal-Williams. Algebraic and Geometric Topology, 2017

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This is an exposition of homotopical results on the geometric realization 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 non-unital topological categories; the effect on classifying spaces of changing the topology on the space of objects; the GroupCompletion Theorem.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/acdfd867650b22fbe1554d28a89b497825750703