On Operads, Bimodules and Analytic Functors

The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory $operatorname{OpdBim}_{mathcal{V}}$ of operad bimodules, that has operads as $0$-cells, operad bimodules as $1$-cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.