Theorems · Theorem · category theory

CategoryTheory.Functor.leibnizPushout_obj_map

∀ {C₁ : Type u₁} {C₂ : Type u₂} {C₃ : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C₁]
  [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] [inst_2 : CategoryTheory.Category.{v₃, u₃} C₃]
  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₃)) [inst_3 : CategoryTheory.Limits.HasPushouts C₃]
  (f₁ : CategoryTheory.Arrow C₁) {X Y : CategoryTheory.Arrow C₂} (sq : X ⟶ Y),
  (F.leibnizPushout.obj f₁).map sq =
    (CategoryTheory.Functor.PushoutObjObj.ofHasPushout F f₁.hom X.hom).mapArrowRight
      (CategoryTheory.Functor.PushoutObjObj.ofHasPushout F f₁.hom Y.hom) sq

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPushouts