Theorems · Theorem · category theory

CategoryTheory.Limits.limitObjIsoLimitCompEvaluation_inv_limit_map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : Type u₁} [inst_1 : CategoryTheory.Category.{v₁, u₁} J]
  {K : Type u₂} [inst_2 : CategoryTheory.Category.{v₂, u₂} K] [inst_3 : CategoryTheory.Limits.HasLimitsOfShape J C]
  {i j : K} (F : CategoryTheory.Functor J (CategoryTheory.Functor K C)) (f : i ⟶ j),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.limitObjIsoLimitCompEvaluation F i).inv
      ((CategoryTheory.Limits.limit F).map f) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.limMap (F.whiskerLeft ((CategoryTheory.evaluation K C).map f)))
      (CategoryTheory.Limits.limitObjIsoLimitCompEvaluation F j).inv

Defined in

Mathlib.CategoryTheory.Limits.FunctorCategory.Basic

Cited by

1 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasLimitsOfShape