
details
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 Setmonad 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 laxalgebraic 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) 127154

