More existence theorems for recursion categories.
type: Item
instance of: scholarly article
title: More existence theorems for recursion categories.
zbMATH Open document ID: 1049.03033
DOI: 10.1016/S0168-0072(03)00060-5
author: Florian Lengyel
published in: Annals of Pure and Applied Logic
publication date: 2004-03-14T00:00:00Z
review text: This paper is a contribution to the study of recursion categories, which are `formal categories of partial maps' equipped with a notion of recursion. Such categories have been extensively studied by A.~Heller, G.~Rosolini, R.~Di~Paola, F.~Montagna and others, and the notation and terminology have now been very highly developed. The present paper makes no concession to the casual reader: here is the statement of its main result. ``Let \(\mathbb C\) and \(\mathbb D\) be iteration categories, and suppose \(\mathbb C\) is separated by an iteration functor \(L:{\mathbb C}\to{\mathbb D}\). If \({\mathbb B}={\mathbb B}(X)\) is a uniformly generated isotypical \(B^{\#}\)-subcategory of \({\mathbb C}(X)\), then \(\text{Tur}({\mathbb B})\) is a recursion category.'' To explain the meaning of all the terms in this result would require a review almost as long as the original paper; however, it can be said that it generalizes a result due to Heller, which is the special case in which \(L\) is the identity functor on \(\mathbb C\). There are also some applications to categories of coalgebras for suitable endofunctors of the category of sets.
Mathematics Subject Classification ID: 03D75
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 18A15
Mathematics Subject Classification ID: 18B99
zbMATH DE Number: 2056204
zbMATH Keywords: Recursion category
zbMATH Keywords: Turing morphism
zbMATH Keywords: Computability
zbMATH Keywords: \(P\)-category
zbMATH Keywords: Coalgebra
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2056204