Theorems · Theorem · category theory
CategoryTheory.Projective.factorThru_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P X E : C} [inst_1 : CategoryTheory.Projective P] (f : P ⟶ X)
(e : E ⟶ X) [inst_2 : CategoryTheory.Epi e],
CategoryTheory.CategoryStruct.comp (CategoryTheory.Projective.factorThru f e) e = f- Cited by
- 8 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.Epistatement and proof · cited by 688
- CategoryTheory.Projectivestatement and proof · cited by 78
- CategoryTheory.Projective.factorThrustatement · cited by 9
- CategoryTheory.Projective.factorsproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ProjectiveResolution.lift_commutesproof · cited by 5
- CategoryTheory.Projective.factorThru_comp_assocproof · cited by 2
- Profinite.lift_liftsproof · cited by 1
- CategoryTheory.Projective.hasLiftingProperty_of_isZeroproof · cited by 1
- CategoryTheory.regularTopology.isSheafFor_regular_of_projectiveproof · cited by 1
- CompHaus.lift_liftsproof · cited by 1