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Yoneda's lemma for internal higher categories

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arxiv 2103.17141 v3 pith:WWN4VJWM submitted 2021-03-31 math.CT math.AT

Louis Martini This is my paper · ORCID
classification math.CTmath.AT
keywords internalcategorieshigherlemmayonedaarbitrarybasicconcepts
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abstract

We develop some basic concepts in the theory of higher categories internal to an arbitrary $\infty$-topos. We define internal left and right fibrations and prove a version of the Grothendieck construction and of Yoneda's lemma for internal categories.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the K-theory of algebraic tori

    math.KT 2025-07 conditional novelty 8.0 of 10

    Algebraic K-theory of a torus is naturally equivalent to the Galois-equivariant homology of its character-lattice torus with equivariant K-theory coefficients.

  2. Approximate Fibrations in Higher Topos Theory

    math.GT 2025-10 accept novelty 7.0 of 10

    Approximate fibrations, previously defined only for topological spaces, are reformulated for higher topoi and shown to coincide with the classical notion for proper maps of locally compact ANRs.

  3. Synthetic perspectives on spaces and categories

    math.CT 2025-10 conditional novelty 3.0 of 10

    A well-referenced exposition of path and arrow induction plus (directed) univalent universes for synthetic spaces and categories, with small strengthened lemmas and a preview of directed univalence.

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