Theorems · Theorem · category theory

CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_desc

Deprecated since 2026-06-21Use CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_lift instead.

∀ {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 (h.functor.obj c)) (s : CategoryTheory.Limits.Cone G),
  ((CategoryTheory.Limits.IsLimit.ofConeEquiv h) P).lift s =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp (h.unitIso.hom.app s).hom
        (h.inverse.map (P.liftConeMorphism (h.functor.obj s))).hom)
      (h.unitIso.inv.app c).hom

Alias of CategoryTheory.Limits.IsLimit.ofConeEquiv_apply_lift.

Defined in

Mathlib.CategoryTheory.Limits.IsLimit

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category