Theorems · Inductive type · category theory

CategoryTheory.Functor.PullbackObjObj

{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] →
            CategoryTheory.Functor C₁ᵒᵖ (CategoryTheory.Functor C₃ C₂) →
              {X₁ Y₁ : C₁} → (X₁ ⟶ Y₁) → {X₃ Y₃ : C₃} → (X₃ ⟶ Y₃) → Type (max u₂ v₂)

Given a bifunctor G : C₁ᵒᵖ ⥤ C₃ ⥤ C₂, and morphisms f₁ : X₁ ⟶ Y₁ in C₁ and f₃ : X₃ ⟶ Y₃ in C₃, this structure contains the data of a pullback of (G.obj (op X₁)).obj X₃ and (G.obj (op Y₁)).obj Y₃ over (G.obj (op X₁)).obj Y₃.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

39 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category