Theorems · Theorem · category theory

CategoryTheory.IsPullback.of_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (F : CategoryTheory.Functor C D) {W X Y Z : C} {f : W ⟶ X} {g : W ⟶ Y} {h : X ⟶ Z} {i : Y ⟶ Z}
  [CategoryTheory.Limits.ReflectsLimit (CategoryTheory.Limits.cospan h i) F],
  CategoryTheory.CategoryStruct.comp f h = CategoryTheory.CategoryStruct.comp g i →
    CategoryTheory.IsPullback (F.map f) (F.map g) (F.map h) (F.map i) → CategoryTheory.IsPullback f g h i

Defined in

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

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsLimit