How to define an operad by generators and relations

Michael Batanin – 18 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.