Operads, clones, and distributive laws

Pierre-Louis Curien (1, 2)

1 PPS - Preuves, Programmes et Systèmes
2 PI.R2 - Design, study and implementation of languages for proofs and programs

We show how non-symmetric operads (or multicategories), symmetric operads, and clones, arise from three suitable monads on Cat, each extending to a (pseudo-)monad on the bicategory of categories and profunctors. We also explain how other previous categorical analyses of operads (via Day's tensor products, or via analytical functors) fit with the profunctor approach.

Domaines: Logique en informatique [cs.LO]; K-théorie et homologie [math.KT]

Pierre-Louis Curien. Operads, clones, and distributive laws. Operads and Universal Algebra : Proceedings of China-France Summer Conference, Jul 2010, Tianjin, China. pp.25-50. ⟨hal-00697065⟩