Theorems · Theorem · category theory

CategoryTheory.Limits.coequalizerComparison_map_desc

∀ {C : Type u} {X Y : C} [inst : CategoryTheory.Category.{v, u} C] (f g : X ⟶ Y) {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (G : CategoryTheory.Functor C D)
  [inst_2 : CategoryTheory.Limits.HasCoequalizer f g]
  [inst_3 : CategoryTheory.Limits.HasCoequalizer (G.map f) (G.map g)] {Z : C} {h : Y ⟶ Z}
  (w : CategoryTheory.CategoryStruct.comp f h = CategoryTheory.CategoryStruct.comp g h),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.coequalizerComparison f g G)
      (G.map (CategoryTheory.Limits.coequalizer.desc h w)) =
    CategoryTheory.Limits.coequalizer.desc (G.map h) ⋯

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Equalizers

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoequalizerCategoryTheory.Limits.HasCoequalizer