Theorems · Theorem · category theory
CategoryTheory.Balanced.isIso_of_mono_of_epi
∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} [self : CategoryTheory.Balanced C] {X Y : C} (f : X ⟶ Y)
[CategoryTheory.Mono f] [CategoryTheory.Epi f], CategoryTheory.IsIso f- Defined in
- Mathlib.CategoryTheory.Balanced
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 32,603
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Monostatement · cited by 893
- CategoryTheory.Epistatement · cited by 688
- CategoryTheory.Balancedstatement and proof · cited by 61
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.isIso_of_mono_of_epiproof · cited by 24
- CategoryTheory.ObjectProperty.IsConservativeFamilyOfPoints.mk'proof · cited by 4
- CategoryTheory.ShortComplex.SnakeInput.isIso_δproof · cited by 3
- CategoryTheory.JointlyFaithful.jointlyReflectsIsomorphismsproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.isIso_fromOpcyclesproof · cited by 0
- CategoryTheory.isRegularEpiCategory_sheafproof · cited by 0
- CategoryTheory.Abelian.SpectralObject.isIso_toCyclesproof · cited by 0