|Location:||MSRI: Baker Board Room|
The fundamental feature of operadic categories is that the objects under study are viewed as algebras over (generalized) operads in a specific operadic category. For instance, operads are algebras over the terminal operad in the operadic category of rooted trees, modular operads are algebras over the terminal operad in the operadic
category of genus-graded connected graphs, wheeled PROPs are algebras over directed graphs, &c. Moreover, operadic categories provide natural environments for Batanin's n-operads, tubings on a graph, decomposition spaces, decalage comonads, and other exotic structures. Operadic categories offer a concise framework for constructing infinity versions of operad-like objects. Operadic Grothendieck's construction is available as a powerful tool for obtaining new operadic categories from old ones.