Theorems · Theorem · category theory
CategoryTheory.Retract.injective
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (h : CategoryTheory.Retract X Y)
[i : CategoryTheory.Injective Y], CategoryTheory.Injective X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.Injectivestatement and proof · cited by 70
- CategoryTheory.Retract.rproof · cited by 34
- CategoryTheory.Retractstatement and proof · cited by 34
- CategoryTheory.Retract.iproof · cited by 34
- CategoryTheory.Category.assoc'proof · cited by 19
- CategoryTheory.Injective.factorsproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- CochainComplex.injective_opcyclesproof · cited by 1