Fernando Abellan, Andrea Gagna and Rune Haugseng
We prove an unstraightening result for lax transformations between functors from an arbitrary (∞, 2)-category to that of (∞, 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 (∞, 2)-categories, to characterize adjoints in (∞, 2)- categories of functors and (op)lax transformations, and to prove a mate correspondence between lax transformations that are componentwise right adjoints and oplax transfor- mations that are componentwise left adjoints, for such transformations among functors between arbitrary (∞, 2)-categories.
