Operads within monoidal pseudo algebras

Applied Categorical Structures, 13(5):389-420, 2005.

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.

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.