Recognition: unknown
Degeneracies in quasi-categories
classification
🧮 math.AT
math.CT
keywords
conditionquasi-categoriessemisimplicialsimplicialspacesadmitsallowscategories
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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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