General Operads and Multicategories

Tom Leinster

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arXiv · math/9810053

General Operads and Multicategories

Tom Leinster

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Abstract

Notions of `operad' and `multicategory' abound. This work provides a single framework in which many of these various notions can be expressed. Explicitly: given a monad * on a category S, we define the term `(S,*)-multicategory', subject to certain conditions on S and *. Different choices of S and * give some of the existing notions of operad and multicategory. We then describe the `algebras' for an (S,*)-multicategory and, finally, present a tentative selection of further developments. Our approach makes possible concise descriptions of Baez and Dolan's opetopes and Batanin's operads; both of these are included.

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Tom Leinster. 1998-10-08. General Operads and Multicategories. https://arxiv.org/abs/math/9810053

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