On the generic solution to \(P(X)\cong X\) in distributive categories
type: Item
instance of: scholarly article
title: On the generic solution to \(P(X)\cong X\) in distributive categories
zbMATH Open document ID: 0890.18005
DOI: 10.1016/S0022-4049(96)00122-3
author: J. Ning
published in: Journal of Pure and Applied Algebra
publication date: 1998-07-01T00:00:00Z
review text: A category \({\mathcal C}\) is distributive if it has finite products and sums such that the canonical morphisms \(X\times Y+ X\times Z\to X \times (Y+Z)\) are isomorphisms. The free distributive category on one generator is given. A polynomial \(P\) in one variable with natural number coefficients can be evaluated at any object \(X\) of the distributive category \({\mathcal C}\) and this value is denoted by \(P(X)\). A \(P\)-algebra in \({\mathcal C}\) is a pair \((X,s)\) of an object \(X\) in \({\mathcal C}\) and a morphism \(s: P(X) \to X\). It is rigid if \(s\) is an isomorphism. A classifying distributive category for \(P\)-algebras, and another one for rigid \(P\)-algebras are build up. For a class of polynomials, concrete descriptions of these categories are given, together with a concrete description of isomorphism classes of objects.
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 68Q65
Mathematics Subject Classification ID: 18C10
zbMATH DE Number: 1121682
zbMATH Keywords: \(P\)-algebras
zbMATH Keywords: generic polynomial
zbMATH Keywords: distributive category
reviewed by: Yves Diers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121682