Operads and polynomial 2-monads

Polynomial 2-monads provide a framework for the discussion of operadic structures, and have been used by Batanin-Berger in the study of when transferred model structures on categories of operads exist. In these talks the theory of polynomial functors was recalled, it was explained how operads can be seen as polynomial monads in a few ways, and how a lot of operadic theory can be recovered from more general ideas in 2-dimensional monad theory. The first talk covered material discussed in the papers

Polynomials in categories with pullbacks

Operads as polynomial 2-monads

and the second could serve as a brief account of what appears in

Internal algebra classifiers as codescent objects of crossed internal categories

Algebraic Kan extensions along morphisms of internal algebra classifiers

Regular patterns, substitudes, Feynman categories and operads (joint with M. Batanin and J. Kock).