Theorems · Theorem · category theory

CategoryTheory.SubobjectRepresentableBy.isPullback

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {Ω : C}
  (h : CategoryTheory.SubobjectRepresentableBy Ω) {U X : C} (m : U ⟶ X) [inst_2 : CategoryTheory.Mono m],
  CategoryTheory.IsPullback m (h.π m) (h.χ m) h.Ω₀.arrow

Defined in

Mathlib.CategoryTheory.Subobject.Classifier.Defs

Cited by

1 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Mono