Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.eq_of_isomorphisms_descendsAlong

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P : CategoryTheory.MorphismProperty C}
  [(CategoryTheory.MorphismProperty.isomorphisms C).DescendsAlong P] [P.IsStableUnderBaseChange]
  [CategoryTheory.Limits.HasEqualizers C] [inst_4 : CategoryTheory.Limits.HasPullbacks C] {X Y S T : C} {f g : X ⟶ Y}
  {s : X ⟶ S} {t : Y ⟶ S} (hf : CategoryTheory.CategoryStruct.comp f t = s)
  (hg : CategoryTheory.CategoryStruct.comp g t = s) (v : T ⟶ S),
  P v →
    CategoryTheory.Limits.pullback.map s v t v f (CategoryTheory.CategoryStruct.id T)
          (CategoryTheory.CategoryStruct.id S) ⋯ ⋯ =
        CategoryTheory.Limits.pullback.map s v t v g (CategoryTheory.CategoryStruct.id T)
          (CategoryTheory.CategoryStruct.id S) ⋯ ⋯ →
      f = g

Defined in

Mathlib.CategoryTheory.MorphismProperty.Descent

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.DescendsAlongCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.Limits.HasEqualizersCategoryTheory.Limits.HasPullbacks