Algebra, Logic and Topology

 

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Author(s)
Maria Manuel Clementino; Walter Tholen;

Title
Metric, Topology and Multicategory - A Common Approach

Abstract
For a symmetric monoidal-closed category V and a suitable monad T on the category of sets, we introduce the notion of reflexive and transitive (T,V)-algebra and show that various old and new structures are instances of such algebras. Lawvere's presentation of a metric space as a V-category is included in our setting, via the Betti-Carboni-Street-Walters interpretation of a V-category as a monad in the bicategory of V-matrices, and so are Barr's presentation of topological spaces as lax algebras, Lowen's approach spaces, and Lambek's multicategories, which enjoy renewed interest in the study of n-categories. As a further example, we introduce a new structure called ultracategory which simultaneously generalizes the notions of topological space and of category.

Journal
J. Pure Appl. Algebra

Volume
179

Year
2003

Issue
1

Page(s)
13-47

 
     
 

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