Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Over.pullbackCongr

{T : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} T] →
    {P Q : CategoryTheory.MorphismProperty T} →
      [inst_1 : Q.IsMultiplicative] →
        {X Y : T} →
          {f : X ⟶ Y} →
            [inst_2 : P.HasPullbacksAlong f] →
              [inst_3 : P.IsStableUnderBaseChangeAlong f] →
                [inst_4 : Q.IsStableUnderBaseChange] →
                  {g : X ⟶ Y} →
                    (h : f = g) →
                      CategoryTheory.MorphismProperty.Over.pullback P Q f ≅
                        CategoryTheory.MorphismProperty.Over.pullback P Q g

If f = g, then base change along f is naturally isomorphic to base change along g.

Defined in

Mathlib.CategoryTheory.MorphismProperty.OverAdjunction

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.HasPullbacksAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChange