Theorems · Inductive type · category theory
CategoryTheory.Balanced
(C : Type u) → [CategoryTheory.Category.{v, u} C] → PropA category is called balanced if any morphism that is both monic and epic is an isomorphism.
- Defined in
- Mathlib.CategoryTheory.Balanced
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by76
Results whose statement or proof uses this declaration.
- CategoryTheory.isIso_of_mono_of_epistatement and proof · cited by 24
- CategoryTheory.ShortComplex.Exact.fIsKernelstatement and proof · cited by 12
- CategoryTheory.ShortComplex.Exact.gIsCokernelstatement and proof · cited by 11
- CategoryTheory.ShortComplex.Exact.lift_fstatement and proof · cited by 9
- CategoryTheory.ShortComplex.Exact.liftstatement and proof · cited by 8
- CategoryTheory.Balanced.isIso_of_mono_of_epistatement and proof · cited by 7
- CategoryTheory.ComposableArrows.Exact.cokerIsoKer'statement and proof · cited by 6
- CategoryTheory.ShortComplex.Exact.descstatement and proof · cited by 6
- CategoryTheory.ShortComplex.Exact.g_descstatement and proof · cited by 5
- CategoryTheory.Sheaf.isLocallySurjective_iff_epi'statement and proof · cited by 5
- CategoryTheory.IsSeparator.isDetectorstatement and proof · cited by 4
- CategoryTheory.ObjectProperty.IsSeparating.isDetectingstatement and proof · cited by 4