Theorems · Theorem · category theory

CategoryTheory.Limits.IsLimit.ofConeEquiv_symm_apply_lift

∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {K : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} K]
  {C : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} C] {F : CategoryTheory.Functor J C} {D : Type u₄}
  [inst_3 : CategoryTheory.Category.{v₄, u₄} D] {G : CategoryTheory.Functor K D}
  (h : CategoryTheory.Limits.Cone G ≌ CategoryTheory.Limits.Cone F) {c : CategoryTheory.Limits.Cone G}
  (P : CategoryTheory.Limits.IsLimit c) (s : CategoryTheory.Limits.Cone F),
  ((CategoryTheory.Limits.IsLimit.ofConeEquiv h).symm P).lift s =
    CategoryTheory.CategoryStruct.comp (h.counitIso.inv.app s).hom
      (h.functor.map (P.liftConeMorphism (h.inverse.obj s))).hom

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

1 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category