Algebraic and Geometric Topology
Mathematical Sciences Publishers
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Ebert, J., & Randal-Williams, O. (2019). Semisimplicial spaces. Algebraic and Geometric Topology, 19 (4), 2099-2150. https://doi.org/10.2140/agt.2019.19.2099
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.
J. Ebert was partially supported by the SFB 878. O. Randal-Williams was supported by EPSRC grant number EP/M027783/1.
External DOI: https://doi.org/10.2140/agt.2019.19.2099
This record's URL: https://www.repository.cam.ac.uk/handle/1810/288687