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Monoidal Topology: A Categorical Approach to Order, Metric, and Topology: Encyclopedia of Mathematics and its Applications, cartea 153

Editat de Dirk Hofmann, Gavin J. Seal, Walter Tholen
en Limba Engleză Hardback – 30 iul 2014
Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly extended from set maps to V-valued relations, the book develops a categorical theory of (T,V)-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book.
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Specificații

ISBN-13: 9781107063945
ISBN-10: 1107063949
Pagini: 518
Ilustrații: 225 exercises
Dimensiuni: 160 x 240 x 33 mm
Greutate: 0.93 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Encyclopedia of Mathematics and its Applications

Locul publicării:New York, United States

Cuprins

Preface; 1. Introduction Robert Lowen and Walter Tholen; 2. Monoidal structures Gavin J. Seal and Walter Tholen; 3. Lax algebras Dirk Hofmann, Gavin J. Seal and Walter Tholen; 4. Kleisli monoids Dirk Hofmann, Robert Lowen, Rory Lucyshyn-Wright and Gavin J. Seal; 5. Lax algebras as spaces Maria Manuel Clementino, Eva Colebunders and Walter Tholen; Bibliography; Tables; Index.

Descriere

Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.