Theorems · Definition · category theory

CategoryTheory.Functor.PullbackObjObj.ofIsTerminal

{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.PreservesLimitsOfShape (CategoryTheory.Discrete PEmpty.{1})
                            (G.obj (Opposite.op X₁))] →
                        [CategoryTheory.Limits.PreservesLimitsOfShape (CategoryTheory.Discrete PEmpty.{1})
                              (G.obj (Opposite.op Y₁))] →
                          CategoryTheory.Limits.IsTerminal Y₃ → G.PullbackObjObj f₁ f₃

A Functor.PullbackObjObj structure for a functor G : C₁ᵒᵖ ⥤ C₃ ⥤ C₂ and morphisms f₁ : X₁ ⟶ Y₁ and f₃ : X₃ ⟶ Y₃ when Y₃ is terminal and both G.obj X₁ and G.obj Y₁ preserve the terminal object.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitsOfShapeCategoryTheory.Limits.PreservesLimitsOfShape