Theorems · Definition · category theory

CategoryTheory.Limits.PreservesPullback.iso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {X Y Z : C} →
            (f : X ⟶ Z) →
              (g : Y ⟶ Z) →
                [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan f g) G] →
                  [inst_3 : CategoryTheory.Limits.HasPullback f g] →
                    [inst_4 : CategoryTheory.Limits.HasPullback (G.map f) (G.map g)] →
                      G.obj (CategoryTheory.Limits.pullback f g) ≅ CategoryTheory.Limits.pullback (G.map f) (G.map g)

If G preserves the pullback of (f,g), then the pullback comparison map for G at (f,g) is an isomorphism.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks

Cited by

19 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback