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math.CT2025
Polygraphs: From Rewriting to Higher Categories
Dimitri Ara, Albert Burroni, Yves Guiraud +3
Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewritin…
math.CT2025
Rewriting techniques for relative coherence
Samuel Mimram
A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal ca…
math.CT2024
Polynomials in homotopy type theory as a Kleisli category
Elies Harington, Samuel Mimram
Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as form…