Theorems · Theorem · category theory
CategoryTheory.Retract.retract
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (self : CategoryTheory.Retract X Y),
CategoryTheory.CategoryStruct.comp self.i self.r = CategoryTheory.CategoryStruct.id X- Defined in
- Mathlib.CategoryTheory.Retract
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Retract.rstatement · cited by 34
- CategoryTheory.Retract.istatement · cited by 34
- CategoryTheory.Retractstatement and proof · cited by 34
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.RetractArrow.retract_rightproof · cited by 4
- CategoryTheory.RetractArrow.retract_leftproof · cited by 4
- CategoryTheory.Retract.retract_assocproof · cited by 2
- CategoryTheory.Retract.hasInjectiveDimensionLTproof · cited by 2
- CategoryTheory.Retract.hasProjectiveDimensionLTproof · cited by 2
- CategoryTheory.Retract.injectiveproof · cited by 1