Theorems · Theorem · category theory

CategoryTheory.Functor.leibnizPullback_map_app

∀ {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]
  (G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)) [inst_3 : CategoryTheory.Limits.HasPullbacks C₂]
  {X Y : (CategoryTheory.Arrow C₁)ᵒᵖ} (sq : X ⟶ Y) (f₃ : CategoryTheory.Arrow C₃),
  (G.leibnizPullback.map sq).app f₃ =
    (CategoryTheory.Functor.PullbackObjObj.ofHasPullback G (Opposite.unop X).hom f₃.hom).mapArrowLeft
      (CategoryTheory.Functor.PullbackObjObj.ofHasPullback G (Opposite.unop Y).hom f₃.hom) sq.unop

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks