Theorems · Theorem · category theory

CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eq

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {P Q : CategoryTheory.MonoOver X} (f : P ⟶ Q),
  CategoryTheory.IsIso (CategoryTheory.Over.Hom.left f.hom) ↔
    CategoryTheory.Subobject.mk P.obj.hom = CategoryTheory.Subobject.mk Q.obj.hom

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.Category

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Cites25

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
CategoryTheory.IsIsostatement and proof · cited by 1,156
CategoryTheory.Overstatement · cited by 935
CategoryTheory.InducedCategory.Hom.homstatement and proof · cited by 850
CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
Eq.leproof · cited by 605

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MonoOver.isIso_iff_subobjectMk_eqproof · cited by 2