Straightening for lax transformations and adjunctions of $(\infty,2)$-categories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911828515225600 |
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| author | Abellán, Fernando Gagna, Andrea Haugseng, Rune |
| author_facet | Abellán, Fernando Gagna, Andrea Haugseng, Rune |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Straightening for lax transformations and adjunctions of $(\infty,2)$-categories Abellán, Fernando Gagna, Andrea Haugseng, Rune Category Theory Algebraic Topology 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. |
| title | Straightening for lax transformations and adjunctions of $(\infty,2)$-categories |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2404.03971 |