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Segal spaces, spans, and semicategories

Abstract

We show that Segal spaces, and more generally category objects in an \infty-category C\mathcal{C}, can be identified with associative algebras in the double \infty-category of spans in C\mathcal{C}. We use this observation to prove that "having identities" is a property of a non-unital (,n)(\infty,n)-category.Comment: Accepted version, 14 page

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