Theorems · Theorem · category theory
CategoryTheory.MonoOver.isIso_iff_isIso_hom_left
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {A B : CategoryTheory.MonoOver X} (f : A ⟶ B),
CategoryTheory.IsIso f ↔ CategoryTheory.IsIso (CategoryTheory.Over.Hom.left f.hom)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.Functor.compproof · cited by 6,529
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
- CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
- CategoryTheory.Over.leftstatement · cited by 541
- CategoryTheory.Over.Hom.leftstatement · cited by 287
- CategoryTheory.Over.forgetproof · cited by 164
- CategoryTheory.MonoOverstatement and proof · cited by 115
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoOver.isIso_iff_subobjectMk_eqproof · cited by 2