English

Degeneracies in quasi-categories

Algebraic Topology 2018-02-27 v3 Category Theory

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).

Keywords

Cite

@article{arxiv.1702.08696,
  title  = {Degeneracies in quasi-categories},
  author = {Wolfgang Steimle},
  journal= {arXiv preprint arXiv:1702.08696},
  year   = {2018}
}

Comments

10 pages; minor corrections

R2 v1 2026-06-22T18:30:34.959Z