On Operads, Bimodules and Analytic Functors

Develops the theory of operads and analytic functors. In particular, the authors 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.

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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.