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Polygraphs: From Rewriting to Higher Categories

Samuel Mimram author Philippe Malbos author Dimitri Ara author Albert Burroni author Yves Guiraud author François Métayer author

Format:Paperback

Publisher:Cambridge University Press

Publishing:31st Mar '25

£90.00

This title is due to be published on 31st March, and will be despatched as soon as possible.

Polygraphs: From Rewriting to Higher Categories cover

The first book to use the unified approach provided by polygraphs to describe the theory of rewriting.

This book, intended for PhD students and researchers, revisits the theory of rewriting and presentations of algebraic structures, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. It introduces the theory step-by-step using low-dimensional illustrations, providing detailed proofs.This is the first book to revisit the theory of rewriting in the context of strict higher categories, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. Illustrated with algorithmic computations on algebraic structures, the only prerequisite in this section is basic category theory. The theory is introduced step-by-step, with detailed proofs. The second half introduces and studies the general notion of n-polygraph, before addressing the homotopy theory of these polygraphs. It constructs the folk model structure on the category on strict higher categories and exhibits polygraphs as cofibrant objects. This allows the formulation of higher-dimensional generalizations of the coherence results developed in the first half. Graduate students and researchers in mathematics and computer science will find this work invaluable.

ISBN: 9781009498982

Dimensions: unknown

Weight: unknown

666 pages