Theorems · Theorem · category theory
CategoryTheory.IsSplitMono.exists_splitMono
∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {X Y : C} {f : X ⟶ Y} [self : CategoryTheory.IsSplitMono f],
Nonempty (CategoryTheory.SplitMono f)There is a splitting
- Defined in
- Mathlib.CategoryTheory.EpiMono
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.IsSplitMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.IsSplitMonostatement and proof · cited by 33
- CategoryTheory.SplitMonostatement · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.retractionproof · cited by 14
- CategoryTheory.IsSplitMono.idproof · cited by 6
- CategoryTheory.Functor.isSplitMono_iffproof · cited by 1
- SimplexCategoryGenRel.isSplitMono_toSimplexCategory_map_of_P_δproof · cited by 0
- CategoryTheory.IsIso.of_mono_retractionproof · cited by 0