Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesPushout.inl_iso_inv

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) {W X Y : C} (f : W ⟶ X) (g : W ⟶ Y)
  [inst_2 : CategoryTheory.Limits.PreservesColimit (CategoryTheory.Limits.span f g) G]
  [inst_3 : CategoryTheory.Limits.HasPushout f g] [inst_4 : CategoryTheory.Limits.HasPushout (G.map f) (G.map g)],
  CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Limits.pushout.inl f g))
      (CategoryTheory.Limits.PreservesPushout.iso G f g).inv =
    CategoryTheory.Limits.pushout.inl (G.map f) (G.map g)

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesColimitCategoryTheory.Limits.HasPushoutCategoryTheory.Limits.HasPushout