Categories with finite limits and stable binary coproducts can be subdirectly decomposed
type: Item
instance of: scholarly article
title: Categories with finite limits and stable binary coproducts can be subdirectly decomposed
zbMATH Open document ID: 0758.18003
DOI: 10.1016/0022-4049(92)90091-S
published in: Journal of Pure and Applied Algebra
publication date: 1992-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 18A35
Mathematics Subject Classification ID: 68Q55
zbMATH DE Number: 60679
zbMATH Keywords: subdirect decomposition
zbMATH Keywords: finitely complete category
zbMATH Keywords: pullback-stable binary coproducts
zbMATH Keywords: semantics of programming languages
zbMATH Keywords: term models
zbMATH Keywords: initial object
zbMATH Keywords: distributive category
author: J. R. B. Cockett
reviewed by: J. Koslowski
MaRDI profile type: Publication
cites work: Q3831000
cites work: List-arithmetic distributive categories: Locoi
cites work: Q3727946
cites work: Data types in distributive categories
description: scientific article; zbMATH DE number 60679