## Algebras of higher operads as enriched categories II

Venue: | In preparation |

Citations: | 6 - 4 self |

### BibTeX

@INPROCEEDINGS{Batanin_algebrasof,

author = {Michael Batanin and Mark Weber},

title = {Algebras of higher operads as enriched categories II},

booktitle = {In preparation},

year = {}

}

### OpenURL

### Abstract

Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads [1] to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as enriched categories for the induced tensor product. This is an important step in reconciling the globular and simplicial approaches to higher category theory, because in the simplicial approaches one proceeds inductively following the idea that a weak (n + 1)category is something like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads.

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Citation Context ...ng like a category enriched in weak n-categories. In this paper we reveal how such an intuition may be formulated in terms of globular operads. 1. Introduction The subject of enriched category theory =-=[9]-=- and 2-category theory was brought to maturity by the efforts of Max Kelly and his collaborators. Max also had a hand in the genesis of the study of operads, and in [10] which for a long time went unp... |

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Citation Context ...pen problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we begin to adapt the machinery of globular operads =-=[1]-=- to this task. We present a general construction of a tensor product on the category of n-globular sets from any normalised (n + 1)-operad A, in such a way that the algebras for A may be recaptured as... |

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Citation Context ...i E i E j E k Xijk E i σ E i E jk Xijk σ E k �� = σ E ij E k Xijk σ �� �� E Xijk ijk E u i E E1Xi E Xi i i ��� �� = σ �� 1 E i Xi Thus a multitensor is very much like a functor-operad in the sense of =-=[13]-=-, except that there are no symmetric group actions with respect to which the substitutions are equivariant 2 . An equivalent formulation of definition(2.1), in the language of [2], is that a multitens... |

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Citation Context ...r a certain monoidal structure, which generalises the substitution tensor product of collections familiar from the theory of operads. Proposition(3.3) is in fact a special case of proposition(2.1) of =-=[7]-=-. Nevertheless we give a self-contained account of proposition(3.3) and related notions, to keep the exposition relatively self-contained and as elementary as possible for our purposes. In section(4) ... |

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