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  1. copying reference from HoTT wiki

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 9th 2022

    I have hyperlinked the abstract, and I have taken the liberty of reformatting as follows – what do you think:


    on internal categories in homotopy type theory and their Rezk completion to univalent categories.

    Abstract. We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of “category” for which equality and equivalence of categories agree. Such categories satisfy a version of the Univalence Axiom, saying that the type of isomorphisms between any two objects is equivalent to the identity type between these objects; we call them “saturated” or “univalent” categories. Moreover, we show that any category is weakly equivalent to a univalent one in a universal way. In homotopical and higher-categorical semantics, this construction corresponds to a truncated version of the Rezk completion for Segal spaces, and also to the stack completion of a prestack.


    diff, v2, current

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