Theorems · Theorem · category theory
CategoryTheory.isIso_of_mono_of_epi
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [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
- 24 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
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 · 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.Balanced.isIso_of_mono_of_epiproof · cited by 7
Cited by24
Results whose statement or proof uses this declaration.
- CategoryTheory.Sheaf.isLocallySurjective_iff_epi'proof · cited by 5
- CategoryTheory.Abelian.isIso_of_epi_of_isIso_of_isIso_of_monoproof · cited by 4
- CategoryTheory.Sheaf.isLocallySurjective_iff_epiproof · cited by 2
- CategoryTheory.isIso_iff_mono_and_epiproof · cited by 2
- CategoryTheory.isIso_of_epi_of_nonzeroproof · cited by 2
- CategoryTheory.ShortComplex.exact_iff_isIso_imageToKernelproof · cited by 2
- CategoryTheory.ObjectProperty.isoModSerre_isInvertedBy_iffproof · cited by 1
- CategoryTheory.ShortComplex.Exact.isIso_f'proof · cited by 1
- HomologicalComplex.HomologySequence.isIso_homologyMap_τ₃proof · cited by 1
- CategoryTheory.ShortComplex.Exact.isIso_g'proof · cited by 1
- FDRep.simple_iff_end_is_rank_oneproof · cited by 1
- SSet.Subcomplex.isIso_toOfSimplex_iffproof · cited by 1