Straightening for lax transformations and adjunctions of (∞, 2)-categories

• Fernando Abellán ^[1] ; Andrea Gagna ^[2] ; Rune Haugseng ^[1]
  1. [1] Norwegian University of Science and Technology

     Norwegian University of Science and Technology

     Noruega

     
  2. [2] Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01084-z
• Enlaces
  • Texto completo
• Resumen

  • We prove an unstraightening result for lax transformations between functors from an arbitrary (∞,2)(\infty, 2)(∞,2)-category to that of (∞,2)(\infty, 2)(∞,2)-categories. We apply this to characterize adjoints in (∞,2)(\infty, 2)(∞,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 (∞,2)(\infty, 2)(∞,2)-categories.

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