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Straightening for lax transformations and adjunctions of $(\infty,2)$-categories

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arxiv 2404.03971 v1 pith:OGPAA2BX submitted 2024-04-05 math.CT math.AT

Fernando Abellán , Andrea Gagna , Rune Haugseng This is my paper · ORCID
classification math.CTmath.AT
keywords inftytransformationscategoriesadjointsfunctorsarbitrarycomponentwiselimits
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abstract

We prove an unstraightening result for lax transformations between functors from an arbitrary $(\infty,2)$-category to that of $(\infty,2)$-categories. We apply this to study partially (op)lax and weighted (co)limits, giving fibrational descriptions of such (co)limits for diagrams valued in $(\infty,2)$-categories, to characterize adjoints in $(\infty,2)$-categories of functors and (op)lax transformations, and to prove a mate correspondence between lax transformations that are componentwise right adjoints and oplax transformations that are componentwise left adjoints, for such transformations among functors between arbitrary $(\infty,2)$-categories.

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Cited by 4 Pith papers

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

  1. Lectures on bar and cobar

    math.AT 2025-07 conditional novelty 7.0 of 10

    The author unifies classical and derived bar and cobar constructions via twisted arrow categories of infinity-operads, giving new existence proofs and recovering classical comparison maps.

  2. On orthogonal factorization systems and double categories

    math.CT 2025-01 conditional novelty 7.0 of 10

    In infinity-category theory, factorization systems embed fully faithfully into double infinity-categories, with an unstraightening theorem and a complete Z/2Z automorphism group for adequate systems.

  3. Fibrations in Oriented Category Theory

    math.AT 2026-07 conditional novelty 6.0 of 10

    The paper establishes several equivalent characterizations of fibrations of (∞,∞)-categories, shows the category of fibrations forms an oriented category, and constructs free, universal, and Grothendieck-construction ...

  4. 2-dimensional Lawvere theories, commutativity, and higher Day convolution

    math.CT 2026-02 conditional novelty 6.0 of 10

    A Lawvere 2-theory with a lax (or pseudo/strict) commutativity structure has a model category that is a closed 2-multicategory, implying a Fox-style comonad and a generalized Day convolution.

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