PROTOPERADS I: COMBINATORICS AND DEFINITIONS

Abstract : This paper is the first of two articles which develop the notion of protoperads. In this one, we construct a new monoidal product on the category of reduced S-modules. We study the associated monoids, called protoperads, which are a generalization of operads. As operads encode algebraic operations with several inputs and one outputs, protoperads encode algebraic operations with the same number of inputs and outputs. We describe the underlying combinatorics of protoperads, and show that there exists a notion of free protoperad. We also show that the monoidal product introduced here is related to Vallette's one on the category of S-bimodules, via the induction functor.
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Pré-publication, Document de travail
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https://hal.archives-ouvertes.fr/hal-01982314
Contributeur : Johan Leray <>
Soumis le : mardi 15 janvier 2019 - 15:39:55
Dernière modification le : mercredi 6 février 2019 - 01:22:59
Document(s) archivé(s) le : mardi 16 avril 2019 - 15:05:59

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  • HAL Id : hal-01982314, version 1
  • ARXIV : 1901.05653

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Johan Leray. PROTOPERADS I: COMBINATORICS AND DEFINITIONS. 2019. ⟨hal-01982314⟩

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