Theorems · Theorem · category theory

CategoryTheory.Functor.PullbackObjObj.ofHasPullback_fst

∀ {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)) {X₁ Y₁ : C₁} (f₁ : X₁ ⟶ Y₁) {X₃ Y₃ : C₃}
  (f₃ : X₃ ⟶ Y₃) [inst_3 : CategoryTheory.Limits.HasPullback ((G.obj (Opposite.op X₁)).map f₃) ((G.map f₁.op).app Y₃)],
  (CategoryTheory.Functor.PullbackObjObj.ofHasPullback G f₁ f₃).fst =
    CategoryTheory.Limits.pullback.fst ((G.obj (Opposite.op X₁)).map f₃) ((G.map f₁.op).app Y₃)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPullback