Theorems · Inductive type · category theory
CategoryTheory.Retract
{C : Type u} → [CategoryTheory.Category.{v, u} C] → C → C → Type vAn object X is a retract of Y if there are morphisms i : X ⟶ Y and r : Y ⟶ X such
that i ≫ r = 𝟙 X.
- Defined in
- Mathlib.CategoryTheory.Retract
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
Cited by63
Results whose statement or proof uses this declaration.
- CategoryTheory.Retract.istatement and proof · cited by 34
- CategoryTheory.Retract.rstatement and proof · cited by 34
- CategoryTheory.RetractArrowproof · cited by 30
- CategoryTheory.ObjectProperty.retractClosureproof · cited by 22
- CategoryTheory.ObjectProperty.monotone_retractClosureproof · cited by 6
- CategoryTheory.ObjectProperty.retractClosure_eq_selfproof · cited by 6
- CategoryTheory.Retract.retractstatement and proof · cited by 6
- CategoryTheory.ObjectProperty.IsStableUnderRetracts.of_retractstatement · cited by 5
- CategoryTheory.Iso.retractstatement · cited by 4
- CategoryTheory.Retract.reflstatement · cited by 3
- CategoryTheory.Retract.transstatement and proof · cited by 3
- CategoryTheory.RetractArrow.leftstatement · cited by 3