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| HAL : hal-00531242, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (02-11-2010) | v2 (13-06-2012) | v3 (08-08-2012) |
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| Higher-dimensional normalisation strategies for acyclicity |
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| Yves Guiraud 1, 2Philippe Malbos 2 |
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| (02/11/2010) |
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| We introduce acyclic track polygraphs, a notion of complete categorical cellular models for small categories: they are polygraphs containing generators, with additional invertible cells for relations and higher-dimensional globular syzygies. We give a rewriting method to realise such a model by proving that a convergent presentation canonically extends to an acyclic track polygraph. For that, we introduce normalising strategies, defined as homotopically coherent ways to relate each cell of a track polygraph to its normal form, and we prove that acyclicity is equivalent to the existence of a normalisation strategy. |
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| 1 : | PAREO (INRIA Lorraine - LORIA) |
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INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Catégories et ensembles Mathématiques/Topologie algébrique Mathématiques/K-théorie et homologie |
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| Rewriting – Homology of small categories – Low-dimensional topology – Identities among relations |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00531242, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00531242 | |
| oai:hal.archives-ouvertes.fr:hal-00531242 | |
| Contributeur : Yves Guiraud | |
| Soumis le : Mardi 2 Novembre 2010, 11:14:18 | |
| Dernière modification le : Mardi 2 Novembre 2010, 12:59:45 | |
