Mathlib Map

Theorems · Theorem · category theory

CategoryTheory.Projective.factors

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {P : C} [self : CategoryTheory.Projective P] {E X : C}
  (f : P ⟶ X) (e : E ⟶ X) [CategoryTheory.Epi e], ∃ f', CategoryTheory.CategoryStruct.comp f' e = f
Defined in
Mathlib.CategoryTheory.Preadditive.Projective.Basic
Cited by
6 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
CategoryTheory.ProjectiveCategoryTheory.Epi
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Projective.factorThru · cited by 9Projective.factorThruCategoryTheory.Projective.factorThru_comp · cited by 8Projective.factorThru_compCategoryTheory.Adjunction.map_projective · cited by 2Adjunction.map_projectiveCategoryTheory.Retract.projective · cited by 1Retract.projectiveCategoryTheory.Adjunction.projective_of_map_projective · cited by 1Adjunction.projective_of_…CategoryTheory.Projective.of_iso · cited by 1Projective.of_isoCategoryTheory.Functor.projective_of_map_projective · cited by 0Functor.projective_of_map…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Epi · cited by 688CategoryTheory.EpiCategoryTheory.Projective · cited by 78CategoryTheory.ProjectiveProjective.factorsCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.