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Theorems · Theorem · category theory

CategoryTheory.Retract.projective

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (h : CategoryTheory.Retract X Y)
  [p : CategoryTheory.Projective Y], CategoryTheory.Projective X
Defined in
Mathlib.CategoryTheory.Preadditive.Projective.Basic
Cited by
1 results in Mathlib
Foundations
Depth 7 from the axioms · uses propext, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Projective
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Around this declaration

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

ModuleCat.hasProjectiveDimensionLT_of_forall_finite · cited by 1ModuleCat.hasProjectiveDi…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.Epi · cited by 688CategoryTheory.EpiCategoryTheory.Projective · cited by 78CategoryTheory.ProjectiveCategoryTheory.Retract.r · cited by 34Retract.rCategoryTheory.Retract.i · cited by 34Retract.iCategoryTheory.Retract · cited by 34CategoryTheory.RetractCategoryTheory.Projective.factors · cited by 6Projective.factorsCategoryTheory.Retract.retract_assoc · cited by 2Retract.retract_assocRetract.projectiveCITED BYCITES

Cites11

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Cited by1

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