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

Fernando Abellán; Andrea Gagna; Rune Haugseng

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arXiv · 2404.03971

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

Fernando Abellán·Andrea Gagna·Rune Haugseng

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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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BibTeX RIS

Fernando Abellán, Andrea Gagna, Rune Haugseng. 2024-04-05. Straightening for lax transformations and adjunctions of $(\infty,2)$-categories. https://arxiv.org/abs/2404.03971

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