Preprint:One setting for all: metric, topology, uniformity, approach structure
This is to announce the availability of the paper "One setting for all: metric, topology, uniformity, approach structure" by M.M. Clementino, D. Hofmann and W. Tholen at http://www.mat.uc.pt/~mmc/preprints/ http://math.yorku.ca/Who/Faculty/Tholen/research.html 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 in T and in V, one establishes a network of functors at the general level which describe the main connections between the structures mentioned in the title. Categories of (T,V)-algebras and of (T,V)-proalgebras turn out to be topological over Set. 25-Nov-2002 10:24:06 -0400,3120;000000000000-00000000
participants (1)
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Walter Tholen