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arXiv · 1702.08696

Degeneracies in quasi-categories

Wolfgang Steimle
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Abstract

In this note we show that a semisimplicial set with the weak Kan condition admits a simplicial structure, provided any object allows an idempotent self-equivalence. Moreover, any two choices of simplicial structures give rise to equivalent quasi-categories. The method is purely combinatorial and extends to semisimplicial objects in other categories; in particular to semi-simplicial spaces satisfying the Segal condition (semi-Segal spaces).

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Wolfgang Steimle. 2017-02-28. Degeneracies in quasi-categories. https://arxiv.org/abs/1702.08696

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