Australian Category Seminar

How to define an operad by generators and relations

Michael Bataninยท18 March 1998

Everybody agrees that the traditional method of defining categories, bicategories, tricategories etc. consists in defining the generators and relations for these algebraic structures. In this talk I try to give precise sense for this statement. For this I show that the theory of generalized computad developed in my paper "Computads for finatery monads on globular sets" can be easely extended to the finatery monads on n-collections. In application to the free operad monad this gives a presentation of every n-operad which consists of an n-computad (in this generelized sense) and a relation on the free operad generated by this computad. We also give examples of such presentation.

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