Theorems · Theorem · category theory

CategoryTheory.SubobjectRepresentableBy.iso_inv_hom_left_comp

∀ {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.CategoryStruct.comp (CategoryTheory.Over.Hom.left (h.iso m).inv.hom) m =
    ((CategoryTheory.Subobject.pullback (h.χ m)).obj h.Ω₀).arrow

Defined in

Mathlib.CategoryTheory.Subobject.Classifier.Defs

Cited by

3 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Mono