Theorems · Inductive type · category theory
CategoryTheory.IsSplitMono
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (X ⟶ Y) → PropIsSplitMono f is the assertion that f admits a retraction
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
Cited by44
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelproof · cited by 25
- CategoryTheory.retractionstatement and proof · cited by 14
- CategoryTheory.IsSplitMono.idstatement and proof · cited by 6
- CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernelstatement and proof · cited by 5
- CategoryTheory.IsSplitMono.exists_splitMonostatement and proof · cited by 4
- CategoryTheory.Limits.coneOfIsSplitMonostatement and proof · cited by 3
- CategoryTheory.epi_iff_isIso_inlproof · cited by 2
- CategoryTheory.IsSplitMono.mk'statement · cited by 2
- CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zerostatement and proof · cited by 1
- CategoryTheory.isSplitMono_of_monostatement · cited by 1
- CochainComplex.isSplitMono_from_singleFunctor_obj_of_injectivestatement · cited by 1
- CategoryTheory.isIso_of_epi_of_isSplitMonostatement and proof · cited by 1