Theorems · Definition · category theory

CategoryTheory.Functor.PullbackObjObj.ofHasPullback

{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) →
                      [CategoryTheory.Limits.HasPullback ((G.obj (Opposite.op X₁)).map f₃) ((G.map f₁.op).app Y₃)] →
                        G.PullbackObjObj f₁ f₃

The PullbackObjObj structure given by the pullback of the limits API.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

21 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPullback