Theorems · Definition · category theory
CategoryTheory.Retract.i
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → CategoryTheory.Retract X Y → (X ⟶ Y)the split monomorphism
- Defined in
- Mathlib.CategoryTheory.Retract
- Cited by
- 34 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.
Cites3
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 · cited by 32,603
- CategoryTheory.Retractstatement and proof · cited by 34
Cited by42
Results whose statement or proof uses this declaration.
- CategoryTheory.Retract.retractstatement · cited by 6
- CategoryTheory.RetractArrow.retract_leftstatement · cited by 4
- CategoryTheory.RetractArrow.retract_rightstatement · cited by 4
- CategoryTheory.Retract.transproof · cited by 3
- CategoryTheory.Retract.hasInjectiveDimensionLTproof · cited by 2
- CategoryTheory.Retract.hasProjectiveDimensionLTproof · cited by 2
- CategoryTheory.NatTrans.retractArrowAppproof · cited by 2
- CategoryTheory.Retract.mapproof · cited by 2
- CategoryTheory.Retract.opproof · cited by 2
- CategoryTheory.Retract.retract_assocstatement and proof · cited by 2
- CategoryTheory.RetractArrow.i_wstatement and proof · cited by 2
- CategoryTheory.RetractArrow.opproof · cited by 2