Name
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. Mathematics Subject Classification: 18C20, 18B30, 54E15. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1023/B:APCS.0000018144.87456.10 | Applied Categorical Structures |
Keywords | Field | DocType |
V,-matrix,V,-promatrix,(,T,V,)-algebra,(,T,V,)-proalgebra,co-Kleisli composition,ordered set,metric space,topological space,uniform space,approach space,prometric space,protopological space,proapproach space,topological category | Uniform space,Discrete mathematics,Topology,Ordered set,Topological space,Approach space,Topological category,Functor,Complete lattice,Metric space,Mathematics | Journal |
Volume | Issue | ISSN |
12 | 2 | 1572-9095 |
Citations | PageRank | References |
19 | 7.10 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Maria Manuel Clementino | 1 | 61 | 25.61 |
| Dirk Hofmann | 2 | 73 | 25.09 |
| Walter Tholen | 3 | 77 | 39.38 |