Theorems · Theorem · category theory
CategoryTheory.isIso_iff_mono_and_epi
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [CategoryTheory.Balanced C] {X Y : C} (f : X ⟶ Y),
CategoryTheory.IsIso f ↔ CategoryTheory.Mono f ∧ CategoryTheory.Epi f- Defined in
- Mathlib.CategoryTheory.Balanced
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.Balancedstatement and proof · cited by 61
- CategoryTheory.isIso_of_mono_of_epiproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.IsSeparating.isDetectingproof · cited by 4
- CategoryTheory.ObjectProperty.SerreClassLocalization.isIso_map_iffproof · cited by 1