On operads, bimodules and analytic functors

Source abstract

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