TY  - BOOK
AU  - Gambino,Nicola
AU  - Joyal,André
TI  - On Operads, Bimodules and Analytic Functors
T2  - Memoirs of the American Mathematical Society
SN  - 9781470441357
AV  - QA169 .G363 2017 
U1  - 512.62 
PY  - 2017///
CY  - Providence
PB  - American Mathematical Society
KW  - Operads
KW  - Functor theory
KW  - Algebra, Homological
KW  - Electronic books
N1  - 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
N2  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5110284
ER  -