Commit 2025-07-15 16:05 ccca4728
View on Github →feat(CategoryTheory/Preadditive/Injective/Basic, CategoryTheory/Preadditive/Projective/Basic): injectivity/projectivity criterion (#27156)
Prove that, if F : C ⥤ D
is a fully faithful functor that preserves monomorphisms (resp. epimorphisms), and if the image by F
of a map f
of C
is injective (resp. projective), then so is f
.
This will be used when F
is the inclusion of a full abelian subcategory to show that we only need to check injectivity/projectivity of a map in the big category.