Categories with sums and right distributive tensor product
type: Item
instance of: scholarly article
title: Categories with sums and right distributive tensor product
zbMATH Open document ID: 1013.18006
DOI: 10.1016/S0022-4049(02)00169-X
author: Anna Labella
published in: Journal of Pure and Applied Algebra
publication date: 2003-03-09T00:00:00Z
review text: Models for parallel and concurrent processes lead quite naturally to the study of monoidal categories. In a previous paper the author has studied a particular category \({\mathcal T}ree\) of trees, equipped with a non-symmetric tensor product, interpreted as a concatenation. This category seems to be very useful to represent (local) behavior of agents able to communicate. The category \({\mathcal T}ree\) is also provided with a coproduct (corresponding to choice between behaviors) and the tensor product is only partially distributive with respect to it, in order to preserve non-determinism. Such a category can be properly defined as the category of the (finite) symmetric category on a free monoid, when this free monoid is considered as a 2-category. The monoidal structure is inherited from the concatenation in the monoid. In the present paper the author proves that for every alphabet \(A\), \({\mathcal T}ree(A)\), the category of finite \(A\)-labeled trees, is equivalent to the free category that is generated by \(A\) and enjoys the afore-mentioned properties. The related category \({\mathcal B}eh(A)\), corresponding to global behaviors, is also proved to be equivalent to the free category that is generated by \(A\) and enjoys a smaller set of properties.
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 68Q10
Mathematics Subject Classification ID: 18B20
zbMATH DE Number: 1878483
zbMATH Keywords: monoidal categories
zbMATH Keywords: non-deterministic parallel computation
zbMATH Keywords: concurrent processes
zbMATH Keywords: 2-category
zbMATH Keywords: concatenation
zbMATH Keywords: alphabet
reviewed by: Andrea Maggiolo-Schettini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1878483