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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. | URI: | https://hdl.handle.net/10316/7757 | DOI: | 10.1023/B:APCS.0000018144.87456.10 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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