From the outset, the theories of ordinary categories and of additive categories were developed in parallel. Indeed additive category theory was dominant in the early days. By additivity for a category I mean that each set of morphisms between two objects (each “hom”) is equipped with the structure of abelian group and composition on either side, with any morphism, distributes over addition: that is to say, the category is enriched in the monoidal category of abelian groups. “Enrichment” in this context is happening to the homs of the category. This enrichment in abelian groups is rather atypical since, for a category with finite products or finite coproducts, it is a property of the category rather than a structure.
|Number of pages||18|
|Journal||Reprints in theory and applications of categories|
|Publication status||Published - 2005|