ENGLISH

Monoidal Topology: A Categorical Approach to Order, Metric, and Topology

By Walter Tholen , Dirk Hofmann , Gavin J. Seal

Book information

Publisher
Cambridge University Press
Year
2014
ISBN
1107063949, 9781107063945
Language
english
Format
PDF
Filesize
5 MB (4822125 bytes)
Series
Encyclopedia of Mathematics and Its Applications 153
Pages
xviii+504\523
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2015-09-16 17:27:26
Pure Mathematics Science Math Algebra Trigonometry

Description

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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