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).