Theorems · Theorem · category theory
CategoryTheory.Injective.comp_factorThru
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J X Y : C} [inst_1 : CategoryTheory.Injective J]
(g : X ⟶ J) (f : X ⟶ Y) [inst_2 : CategoryTheory.Mono f],
CategoryTheory.CategoryStruct.comp f (CategoryTheory.Injective.factorThru g f) = g- Cited by
- 10 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses Classical.choice
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Injectivestatement and proof · cited by 70
- CategoryTheory.Injective.factorThrustatement · cited by 12
- CategoryTheory.Injective.factorsproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.Exact.comp_descToInjectiveproof · cited by 6
- CategoryTheory.InjectiveResolution.desc_commutesproof · cited by 4
- CategoryTheory.Abelian.epiWithInjectiveKernel_iffproof · cited by 3
- CategoryTheory.Injective.hasLiftingProperty_of_isZeroproof · cited by 2
- FDRep.simple_iff_end_is_rank_oneproof · cited by 1
- CategoryTheory.Abelian.has_injective_coseparatorproof · cited by 1
- CategoryTheory.Injective.comp_factorThru_assocproof · cited by 1
- CategoryTheory.Injective.injective_of_adjointproof · cited by 0