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| HAL : hal-00702041, version 1 |
| arXiv : 1101.3064 |
| DOI : 10.1016/j.jpaa.2012.02.039 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Pure and Applied Algebra 216, 8-9 (2012) 2029-2048 |
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| Monads with arities and their associated theories |
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| Clemens Bergerpaul-andré melliès 1 |
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| (08/2012) |
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| After a review of the concept of "monad with arities" we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere's algebraic theories to a general correspondence between monads and theories for a given category with arities. As application we determine arities for the free groupoid monad on involutive graphs and recover the symmetric simplicial nerve characterisation of groupoids. |
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| 1 : | Preuves, Programmes et Systèmes (PPS) |
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CNRS : UMR7126 – Université Paris VII - Paris Diderot |
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| 2 : | Macquarie University |
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University of Sydney |
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| Domaine | : | Mathématiques/Catégories et ensembles |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1101.3064 |
| hal-00702041, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00702041 | |
| oai:hal.archives-ouvertes.fr:hal-00702041 | |
| Contributeur : Paul-André Melliès | |
| Soumis le : Mardi 29 Mai 2012, 10:09:19 | |
| Dernière modification le : Mardi 29 Mai 2012, 10:09:19 | |
