Operads, clones, and distributive laws

2012/05/14 by Curien, Pierre-Louis
#Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #K-Theory and Homology (math.KT) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.1205.3050

Abstract

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.

Related

• General Operads and Multicategories
• Operads as double functors
• Operads, tensor products, and the categorical Borel construction
• Operads as polynomial 2-monads
• Operads in Higher-Dimensional Category Theory