Theorems · Theorem · category theory

CategoryTheory.Functor.leibnizPullback_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]
  (G : CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂)) [inst_3 : CategoryTheory.Limits.HasPullbacks C₂]
  (f₁ : (CategoryTheory.Arrow C₁)ᵒᵖ) {X Y : CategoryTheory.Arrow C₃} (sq : X ⟶ Y),
  (G.leibnizPullback.obj f₁).map sq =
    (CategoryTheory.Functor.PullbackObjObj.ofHasPullback G (Opposite.unop f₁).hom X.hom).mapArrowRight
      (CategoryTheory.Functor.PullbackObjObj.ofHasPullback G (Opposite.unop f₁).hom Y.hom) sq

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