On Operads, Bimodules and Analytic Functors.

Cover -- Title page -- Introduction -- Chapter 1. Background -- 1.1. Review of bicategory theory -- 1.2. \catV-categories and presentable \catV-categories -- 1.3. Distributors -- Chapter 2. Monoidal distributors -- 2.1. Monoidal \catV-categories and \catV-rigs -- 2.2. Monoidal distributors -- 2.3. Symmetric monoidal \catV-categories and symmetric \catV-rigs -- 2.4. Symmetric monoidal distributors -- Chapter 3. Symmetric sequences -- 3.1. Free symmetric monoidal \catV-categories -- 3.2. -distributors -- 3.3. Symmetric sequences and analytic functors -- 3.4. Cartesian closure of categorical symmetric sequences -- Chapter 4. The bicategory of operad bimodules -- 4.1. Monads, modules and bimodules -- 4.2. Tame bicategories and bicategories of bimodules -- 4.3. Monad morphisms and bimodules -- 4.4. Tameness of bicategories of symmetric sequences -- 4.5. Analytic functors -- Chapter 5. Cartesian closure of operad bimodules -- 5.1. Cartesian closed bicategories of bimodules -- 5.2. Monad theory in tame bicategories -- 5.3. Monad theory in bicategories of bimodules -- 5.4. Bicategories of bimodules as Eilenberg-Moore completions -- Appendix A. A compendium of bicategorical definitions -- Appendix B. A technical proof -- B.1. Preliminaries -- B.2. The proof -- Bibliography -- Back Cover.

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.

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