Theorems · Theorem · category theory
CategoryTheory.Injective.hasLiftingProperty_of_isZero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A B I Z : C} (i : A ⟶ B) [CategoryTheory.Mono i]
[CategoryTheory.Injective I] (p : I ⟶ Z), CategoryTheory.Limits.IsZero Z → CategoryTheory.HasLiftingProperty i p- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Limits.IsZerostatement and proof · cited by 306
- CategoryTheory.CommSqproof · cited by 158
- CategoryTheory.Injectivestatement and proof · cited by 70
- CategoryTheory.HasLiftingPropertystatement · cited by 50
- CategoryTheory.Limits.IsZero.eq_of_tgtproof · cited by 46
- CategoryTheory.Injective.factorThruproof · cited by 12
- CategoryTheory.Injective.comp_factorThruproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.injective_iff_rlp_monomorphisms_of_isZeroproof · cited by 1
- CategoryTheory.Abelian.epiWithInjectiveKernel.hasLiftingPropertyproof · cited by 0