CategoryTheory.ShortComplex.abelianImageToKernel.proof_4

theorem CategoryTheory.ShortComplex.abelianImageToKernel.proof_4 : ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Abelian C] (S : CategoryTheory.ShortComplex C), CategoryTheory.CategoryStruct.comp (CategoryTheory.Abelian.image.ι S.f) S.g = 0

This theorem is a statement in the field of category theory, specifically within the context of abelian categories. It says that for any short complex `S`, the composition of the morphism `ι` from the image of `S.f` and the morphism `S.g` is the zero morphism. Here, `S.f` and `S.g` are morphisms in an abelian category `C`, and `CategoryTheory.Abelian.image.ι S.f` denotes the inclusion from the image of `S.f` into the codomain. The composition of these morphisms is done using the `CategoryTheory.CategoryStruct.comp` function. In more mathematical terms, if we denote `ι` as the inclusion map, it says that `ι(S.f) ∘ S.g = 0` in the category `C`.

More concisely: In an abelian category, for any short complex `S`, the composition of the morphism `S.g` with the inclusion `ι` of the image of `S.f` is the zero morphism.