Polynomial functors and opetopes

Joachim Kock*, André Joyal, Michael Batanin, J. F. Mascari

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    29 Citations (Scopus)

    Abstract

    We give an elementary and direct combinatorial definition of opetopes in terms of trees, well-suited for graphical manipulation and explicit computation. To relate our definition to the classical definition, we recast the Baez-Dolan slice construction for operads in terms of polynomial monads: our opetopes appear naturally as types for polynomial monads obtained by iterating the Baez-Dolan construction, starting with the trivial monad. We show that our notion of opetope agrees with Leinster's. Next we observe a suspension operation for opetopes, and define a notion of stable opetopes. Stable opetopes form a least fixpoint for the Baez-Dolan construction. A final section is devoted to example computations, and indicates also how the calculus of opetopes is well-suited for machine implementation.

    Original languageEnglish
    Pages (from-to)2690-2737
    Number of pages48
    JournalAdvances in Mathematics
    Volume224
    Issue number6
    DOIs
    Publication statusPublished - Aug 2010

    Fingerprint

    Dive into the research topics of 'Polynomial functors and opetopes'. Together they form a unique fingerprint.

    Cite this