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Title: One Setting for All: Metric, Topology, Uniformity, Approach Structure
Authors: Clementino, Maria 
Hofmann, Dirk 
Tholen, Walter 
Issue Date: 2004
Citation: Applied Categorical Structures. 12:2 (2004) 127-154
Abstract: 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.
DOI: 10.1023/B:APCS.0000018144.87456.10
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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