A formal language for cyclic operads

Pierre-Louis Curien (1, 2) , Jovana Obradovic (2, 1)

1 PI.R2 - Design, study and implementation of languages for proofs and programs
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We give a complete proof of the equivalence between the unbiased and biased definitions of cyclic operads, through a lambda-calculus-style formal language, called the mu-syntax, and a new formalism of trees that provides a crisp description of the monad of unrooted trees (whose nodes are decorated with operadic operations).

Mots clés: Unrooted trees; Rewriting; Monad; Operads

Domaines: Topologie algébrique [math.AT]; Logique en informatique [cs.LO]

Pierre-Louis Curien, Jovana Obradovic. A formal language for cyclic operads. Higher Structures, 2017. ⟨hal-01278214⟩