Theorems · Inductive type · category theory
CategoryTheory.Injective
{C : Type u₁} → [CategoryTheory.Category.{v₁, u₁} C] → C → PropAn object J is injective iff every morphism into J can be obtained by extending a monomorphism.
- Cited by
- 70 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 by90
Results whose statement or proof uses this declaration.
- CategoryTheory.Injective.factorThrustatement and proof · cited by 12
- CategoryTheory.Injective.comp_factorThrustatement and proof · cited by 10
- CategoryTheory.Injective.factorsstatement and proof · cited by 8
- CategoryTheory.isInjectiveproof · cited by 6
- CategoryTheory.ShortComplex.Exact.comp_descToInjectivestatement and proof · cited by 6
- CategoryTheory.Abelian.epiWithInjectiveKernelproof · cited by 4
- CategoryTheory.ShortComplex.Exact.descToInjectivestatement and proof · cited by 4
- CategoryTheory.Abelian.Ext.eq_zero_of_injectivestatement and proof · cited by 4
- Module.injective_iff_injective_objectstatement and proof · cited by 3
- CategoryTheory.Injective.of_isostatement and proof · cited by 3
- CategoryTheory.Abelian.epiWithInjectiveKernel_iffstatement and proof · cited by 3
- CategoryTheory.InjectiveResolution.selfstatement and proof · cited by 3