New PDF release: Monoidal Topology: A Categorical Approach to Order, Metric

By Dirk Hofmann,Gavin J. Seal,Walter Tholen

ISBN-10: 1107063949

ISBN-13: 9781107063945

Monoidal Topology describes an lively examine zone that, after numerous prior proposals on how you can axiomatize 'spaces' by way of convergence, started to emerge at the start of the millennium. It combines Barr's relational presentation of topological areas by way of ultrafilter convergence with Lawvere's interpretation of metric areas as small different types enriched over the prolonged genuine half-line. consequently, built with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly prolonged from set maps to V-valued family members, the ebook develops a express thought of (T,V)-algebras that's encouraged concurrently by means of its metric and topological roots. The ebook highlights particularly the prestigious position of equationally outlined buildings in the given lax-algebraic context and provides quite a few new effects starting from topology and process conception to area idea. all of the worthwhile pre-requisites so as and type concept are offered within the book.

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Monoidal Topology: A Categorical Approach to Order, Metric and Topology (Encyclopedia of Mathematics and its Applications) by Dirk Hofmann,Gavin J. Seal,Walter Tholen

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