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  3. Polygraphs: From Rewriting to Higher Categories
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2025
      April 2025
      ISBN:
      9781009498968
      9781009498982
      DOI:
      https://doi.org/10.1017/9781009498968
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      1.04kg, 666 Pages
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
      Series:
      London Mathematical Society Lecture Note Series (495)
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
    Series:
    London Mathematical Society Lecture Note Series (495)
    Information

    Book description

    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.

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    Contents

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    Contents

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