Coherence in monoidal track categories

Yves Guiraud 1, 2, 3, * Philippe Malbos 1
* Corresponding author
3 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an asphericity problem for a track category and we use rewriting methods on polygraphs to solve it. The setting is extended to more general coherence problems, seen as 3-dimensional word problems in a track category, including the case of braided monoidal categories.
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  • HAL Id : hal-00470795, version 2

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Yves Guiraud, Philippe Malbos. Coherence in monoidal track categories. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2012, 22 (6), pp.931-969. ⟨hal-00470795v2⟩

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