Monoidal Topology

A Categorical Approach to Order, Metric, and Topology

Author: Dirk Hofmann,Gavin J. Seal,Walter Tholen

Publisher: Cambridge University Press

ISBN: 1139993283

Category: Mathematics

Page: N.A

View: 1795

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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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Programming Languages and Systems

28th European Symposium on Programming, ESOP 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, Prague, Czech Republic, April 6–11, 2019, Proceedings

Author: Luís Caires

Publisher: Springer

ISBN: 3030171841

Category: Computers

Page: 816

View: 7846

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This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019.
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Quasi-Hopf Algebras

A Categorical Approach

Author: Daniel Bulacu,Stefaan Caenepeel,Florin Panaite,Freddy Van Oystaeyen

Publisher: Cambridge University Press

ISBN: 1108427014

Category: Mathematics

Page: 544

View: 8637

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This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
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