On Operads, Bimodules and Analytic Functors.
Gambino, Nicola.
On Operads, Bimodules and Analytic Functors. - 1st ed. - 1 online resource (122 pages) - Memoirs of the American Mathematical Society ; v.249 . - Memoirs of the American Mathematical Society .
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_} 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.
9781470441357
Operads.
Functor theory.
Algebra, Homological.
Electronic books.
QA169 .G363 2017
512.62
On Operads, Bimodules and Analytic Functors. - 1st ed. - 1 online resource (122 pages) - Memoirs of the American Mathematical Society ; v.249 . - Memoirs of the American Mathematical Society .
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_} 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.
9781470441357
Operads.
Functor theory.
Algebra, Homological.
Electronic books.
QA169 .G363 2017
512.62