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On operads, bimodules and analytic functors

About this Title

Nicola Gambino and André Joyal

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 249, Number 1184
ISBNs: 978-1-4704-2576-0 (print); 978-1-4704-4135-7 (online)
Published electronically: August 9, 2017
Keywords:Operad, bimodule, bicategory, symmetric sequence, analytic functor

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Table of Contents


  • Introduction
  • Chapter 1. Background
  • Chapter 2. Monoidal distributors
  • Chapter 3. Symmetric sequences
  • Chapter 4. The bicategory of operad bimodules
  • Chapter 5. Cartesian closure of operad bimodules
  • Appendix A. A compendium of bicategorical definitions
  • Appendix B. A technical proof


We develop further the theory of operads and analytic functors. In particular, we introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -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.

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