Polynomial functors and opetopes
Research output: Contribution to journal › Journal article › Research › peer-review
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. (C) 2010 Elsevier Inc All rights reserved
Original language | English |
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Journal | Advances in Mathematics |
Volume | 224 |
Issue number | 6 |
Pages (from-to) | 2690-2737 |
Number of pages | 48 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 20 Aug 2010 |
Externally published | Yes |
- Polynomial functor, Tree, Opetope, Monad, WEAK N-CATEGORIES, TREES
Research areas
ID: 331502175