Segal spaces, spans, and semicategories

  title={Segal spaces, spans, and semicategories},
  author={R. Haugseng},
  journal={arXiv: Algebraic Topology},
  • R. Haugseng
  • Published 2019
  • Mathematics
  • arXiv: Algebraic Topology
We show that Segal spaces, and more generally category objects in an $\infty$-category $\mathcal{C}$, can be identified with associative algebras in the double $\infty$-category of spans in $\mathcal{C}$. We use this observation to prove that "having identities" is a property of a non-unital $(\infty,n)$-category. 
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