One Setting for All: Metric, Topology, Uniformity, Approach Structure
| Citations: | 12 - 6 self |
BibTeX
@MISC{Clementino_onesetting,
author = {Maria Manuel Clementino and Dirk Hofmann and Walter Tholen},
title = {One Setting for All: Metric, Topology, Uniformity, Approach Structure},
year = {}
}
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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.
