Theorems · Theorem · category theory

CategoryTheory.preservesColimitNatIso_hom_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J]
  [inst_3 : CategoryTheory.Limits.PreservesColimitsOfShape J G] [inst_4 : CategoryTheory.Limits.HasColimitsOfShape J D]
  [inst_5 : CategoryTheory.Limits.HasColimitsOfShape J C] (X : CategoryTheory.Functor J C),
  (CategoryTheory.preservesColimitNatIso G).hom.app X = (CategoryTheory.preservesColimitIso G X).hom

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Limits

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShape