Categories with finite limits and stable binary coproducts can be subdirectly decomposed
This article shows nicely that it pays to take application-induced constraints seriously. The application here is theoretical computer science, more precisely the semantics of programming languages. The initial categories that are gaining importance as term models in this area, besides being finitely complete, preferably ought to have binary coproducts that are pullback-stable and ``disjoint''. However, disjointness depends on the existence of an initial object which is usually absent in real life models. For a categorically-minded computer scientist this presents a real challenge. The author meets it by showing that the categories of interest can be subdirectly decomposed into a distribution lattice and a distributive category (as introduced by Lawvere and Schanuel, and lately of increasing importance is categorical computer science), which has the desired properties. Here category theory is applied to a real computer science problem in a non-superficial way, demonstrating the value of serious dialogue between both disciplines.
scientific article; zbMATH DE number 60679