Theorems · Theorem · category theory

CategoryTheory.Functor.PreservesProjectiveObjects.projective_obj

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
  {F : CategoryTheory.Functor C D} [self : F.PreservesProjectiveObjects] {X : C},
  CategoryTheory.Projective X → CategoryTheory.Projective (F.obj X)

Defined in: Mathlib.CategoryTheory.Preadditive.Projective.Preserves
Cited by: 2 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.Functor.PreservesProjectiveObjects

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Cites5

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
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Projectivestatement · cited by 78
CategoryTheory.Functor.PreservesProjectiveObjectsstatement and proof · cited by 7

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Functor.projective_obj_of_projectiveproof · cited by 1
CategoryTheory.Functor.mapExt_bijective_of_preservesProjectiveObjectsproof · cited by 0