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Monoidal closed structures on categories with constant maps

Part of: Categories with structure Basic constructions Special categories

Published online by Cambridge University Press:  09 April 2009

Alessandro Logar  and
Fabio Rossi
Alessandro Logar
Affiliation:
Istituto di Mathematica Università Degli Studi di TriestePiazzale Europa, 1 34100-Trieste, Italy
Fabio Rossi
Affiliation:
Istituto di Mathematica Università Degli Studi di TriestePiazzale Europa, 1 34100-Trieste, Italy
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Abstract

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The purpose of this paper is to study the so-called canonical monoidal closed structures on concrete categories with constant maps. First of all we give an example of a category of this kind where there exists a non canonical monoidal closed structure. Later, we give a technique to construct a class of suitable full subcategories of the category of T0-spaces, such that all monoidal closed structures on them are canonical. Finally we show that “almost all” useful categories of topological compact spaces admit no monoidal closed structures whatsoever.

MSC classification

Secondary: 18D15: Closed categories (closed monoidal and Cartesian closed categories, etc.) 18B30: Categories of topological spaces and continuous mappings 54B30: Categorical methods
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 175 - 185
Copyright
Copyright © Australian Mathematical Society 1985

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