Cartesian closed topological categories and tensor products
type: Item
instance of: scholarly article
title: Cartesian closed topological categories and tensor products
zbMATH Open document ID: 1077.18006
author: Gavin J. Seal
published in: Applied Categorical Structures
publication date: 2005-06-16T00:00:00Z
review text: In the last years, the concept of Cartesian closed category has proved its utility not only for Mathematics but also for Computer Science. It is useful to study its properties in order to obtain more applications. In this context, this paper deals with the relationships between the tensor closedness of \({\mathcal M}od_{R}({\mathcal X})\), the category of \(R\)-module objects in a category \({\mathcal X}\) (where \(R\) is itself a ring object of \({\mathcal X}\)) and the Cartesian closedness of \({\mathcal X}\). It is shown, for example, that if \({\mathcal X}\) is Cartesian closed topological, then \({\mathcal M}od_{R}({\mathcal X})\) is tensor closed, and, moreover, is a monoidal category w.r.t. the same tensor product.
reviewed by: Viorel Mihai Gontineac
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 2176362
zbMATH Keywords: Cartesian closed category
zbMATH Keywords: monoidal closed category
zbMATH Keywords: topological category
zbMATH Keywords: tensor product
zbMATH Keywords: module object
MaRDI profile type: Publication
full work available at URL: s10485-004-2940-7
OpenAlex ID: W1998540863
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DOI: 10.1007/S10485-004-2940-7
description: scientific article; zbMATH DE number 2176362