Theorems · Definition · category theory

CategoryTheory.Limits.pullbackComparison

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      {D : Type u₂} →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
          (G : CategoryTheory.Functor C D) →
            (f : X ⟶ Z) →
              (g : Y ⟶ Z) →
                [inst_2 : CategoryTheory.Limits.HasPullback f g] →
                  [inst_3 : 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)

The comparison morphism for the pullback of f,g. This is an isomorphism iff G preserves the pullback of f,g; see Mathlib/CategoryTheory/Limits/Preserves/Shapes/Pullbacks.lean

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

13 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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