equivOfNatIsoOfIso — Mathlib

English

Similar to 70019, but with a focus on the reverse direction of the equivalence induced by α between cones and their IsLimit structures.

Русский

Повторение идеи 70019: эквивалентость IsLimit через α между конусами и соответствующими ограничениями.

LaTeX

$$$ IsLimit c \\simeq IsLimit d \\text{ via } (postcompose \\alpha.hom) \\text{ and } w $$$

Lean4

/-- Constructing an equivalence `IsLimit c ≃ IsLimit d` from a natural isomorphism
between the underlying functors, and then an isomorphism between `c` transported along this and `d`.
-/
def equivOfNatIsoOfIso {F G : J ⥤ C} (α : F ≅ G) (c : Cone F) (d : Cone G) (w : (Cones.postcompose α.hom).obj c ≅ d) :
    IsLimit c ≃ IsLimit d :=
  (postcomposeHomEquiv α _).symm.trans (equivIsoLimit w)

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