On operads, bimodules and analytic functors

Abstract

We develop further the theory of operads and analytic functors. In particular, we introduce a bicategory that has operads as 0-cells, operad bimodules as 1-cells and operad bimodule maps as 2-cells, and prove that this bicategory is cartesian closed. In order to obtain this result, we extend the theory of distributors and the formal theory of monads.

v2: introduction rewritten, some material reorganised, terminology revised (we now call "tame bicategories" the bicategories with local reflexive coequalizers, which are preserved by composition on both sides), 109 pages, to appear in Memoirs of the AMS

References in corpus (1)

• The periodic table of $n$-categories for low dimensions II: degenerate tricategories

Cited by in corpus (10)

• Admissibility and rectification of colored symmetric operads
• Coend calculus
• Relative pseudomonads, Kleisli bicategories, and substitution monoidal structures
• Endofunctors and Poincaré-Birkhoff-Witt theorems
• Involutive categories, colored $\ast$-operads and quantum field theory
• Cofree coalgebras over operads and representative functions
• Automata and coalgebras in categories of species
• Free and based path groupoids
• A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras
• The Grothendieck Construction in Categorical Network Theory