Theorems · Theorem · category theory

CategoryTheory.IsPullback.of_iso_pullback

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P X Y Z : C} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z}
  {g : Y ⟶ Z},
  CategoryTheory.CommSq fst snd f g →
    ∀ [inst_1 : CategoryTheory.Limits.HasPullback f g] (i : P ≅ CategoryTheory.Limits.pullback f g),
      CategoryTheory.CategoryStruct.comp i.hom (CategoryTheory.Limits.pullback.fst f g) = fst →
        CategoryTheory.CategoryStruct.comp i.hom (CategoryTheory.Limits.pullback.snd f g) = snd →
          CategoryTheory.IsPullback fst snd f g

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.Basic

Cited by

10 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback