Theorems · Theorem · category theory

CategoryTheory.Subobject.pullback_obj

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {X Y : C}
  (f : Y ⟶ X) (x : CategoryTheory.Subobject X),
  (CategoryTheory.Subobject.pullback f).obj x =
    CategoryTheory.Subobject.mk (CategoryTheory.Limits.pullback.snd x.arrow f)

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

1 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks