Algebra, Logic and Topology

 

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Author(s)
Dirk Hofmann; Maria Manuel Clementino; Walter Tholen;

Title
One setting for all: metric, topology, uniformity, approach structure

Abstract
For a complete lattice V which, as a category, is monoidal closed, and for a suitable Set-monad T we consider (T,V)-algebras and introduce (T,V)-proalgebras, in generalization of Lawvere's presentation of metric spaces and
Barr's presentation of topological spaces. In this lax-algebraic setting, uniform spaces appear as proalgebras. Since the corresponding categories behave functorially both in T and in V, one establishes a network of functors at the general level which describe the basic connections between the structures mentioned by the title. Categories of (T,V)-algebras and of (T,V)-proalgebras turn out to be topological over Set.

Journal
Applied Categorical Structures

Volume
12

Year
2004

Issue
2

Page(s)
127-154

 
     
 

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