Theorems · Theorem · category theory
CategoryTheory.isIso_of_epi_of_isSplitMono
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : Y ⟶ X) [CategoryTheory.Epi f]
[CategoryTheory.IsSplitMono f], CategoryTheory.IsIso fA split mono which is epi is an iso.
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Epistatement and proof · cited by 688
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.IsSplitMonostatement and proof · cited by 33
- CategoryTheory.Category.assoc'proof · cited by 19
- CategoryTheory.retractionproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.mem_essImage_of_unit_isSplitMonoproof · cited by 0