Theorems · Theorem · category theory

CategoryTheory.Limits.hasPullback_of_preservesPullback

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) {X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z)
  [CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan f g) G] [CategoryTheory.Limits.HasPullback f g],
  CategoryTheory.Limits.HasPullback (G.map f) (G.map g)

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks

Cited by

5 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.PreservesLimitCategoryTheory.Limits.HasPullback