Polygraphs: From Rewriting to Higher Categories

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

ISBN 10: 1009498983 / ISBN 13: 9781009498982

Published by Cambridge University Press CUP, 2025

Seller Inventory # 26403556012

Synopsis:

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.

About the Authors: Dimitri Ara is Associate Professor at Aix-Marseille Université.

Albert Burroni is Associate Researcher at Université Paris Cité.

Yves Guiraud is Researcher at Université Paris Cité.

Philippe Malbos is Professor at Université Claude Bernard Lyon 1.

Francois Métayer is Associate Professor Emeritus at Université Paris Cité.

Bibliographic Details

Title: Polygraphs: From Rewriting to Higher ...
Publisher: Cambridge University Press CUP
Publication Date: 2025
Binding: Soft cover
Condition: New