Operads within Monoidal Pseudo Algebras

A general notion of operad is given, which includes: (1) the operads that arose in algebraic topology in the 1970’s to characterise loop spaces. (2) the higher operads of Michael Batanin [Bat98]. (3) braided and symmetric analogues of Batanin’s operads which are likely to be important in the study of weakly symmetric higher dimensional monoidal categories. The framework of this paper, links together 2-dimensional monad theory, operads, and higher dimensional algebra, in a natural way.