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Monoidal Topology Dirk Hofmann

Monoidal Topology

Dirk Hofmann

Published September 2nd 2014
ISBN : 9781322066899
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 About the Book 

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 Barrs relational presentation ofMoreMonoidal 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 Barrs relational presentation of topological spaces in terms of ultrafilter convergence with Lawveres 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