Polynomial functors and opetopes

Research output: Contribution to journal › Journal article › Research › peer-review

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Polynomial functors and opetopes. / Kock, Joachim; Joyal, Andre; Batanin, Michael; Mascari, Jean-Francois.

In: Advances in Mathematics, Vol. 224, No. 6, 20.08.2010, p. 2690-2737.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kock, J, Joyal, A, Batanin, M & Mascari, J-F 2010, 'Polynomial functors and opetopes', Advances in Mathematics, vol. 224, no. 6, pp. 2690-2737. https://doi.org/10.1016/j.aim.2010.02.012

APA

Kock, J., Joyal, A., Batanin, M., & Mascari, J-F. (2010). Polynomial functors and opetopes. Advances in Mathematics, 224(6), 2690-2737. https://doi.org/10.1016/j.aim.2010.02.012

Vancouver

Kock J, Joyal A, Batanin M, Mascari J-F. Polynomial functors and opetopes. Advances in Mathematics. 2010 Aug 20;224(6):2690-2737. https://doi.org/10.1016/j.aim.2010.02.012

Author

Kock, Joachim ; Joyal, Andre ; Batanin, Michael ; Mascari, Jean-Francois. / Polynomial functors and opetopes. In: Advances in Mathematics. 2010 ; Vol. 224, No. 6. pp. 2690-2737.

Bibtex

@article{a5a08102ea494602946647cb95f19f00,
title = "Polynomial functors and opetopes",
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. (C) 2010 Elsevier Inc All rights reserved",
keywords = "Polynomial functor, Tree, Opetope, Monad, WEAK N-CATEGORIES, TREES",
author = "Joachim Kock and Andre Joyal and Michael Batanin and Jean-Francois Mascari",
year = "2010",
month = aug,
day = "20",
doi = "10.1016/j.aim.2010.02.012",
language = "English",
volume = "224",
pages = "2690--2737",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",
number = "6",

}

RIS

TY - JOUR

T1 - Polynomial functors and opetopes

AU - Kock, Joachim

AU - Joyal, Andre

AU - Batanin, Michael

AU - Mascari, Jean-Francois

PY - 2010/8/20

Y1 - 2010/8/20

N2 - 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

AB - 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

KW - Polynomial functor

KW - Tree

KW - Opetope

KW - Monad

KW - WEAK N-CATEGORIES

KW - TREES

U2 - 10.1016/j.aim.2010.02.012

DO - 10.1016/j.aim.2010.02.012

M3 - Journal article

VL - 224

SP - 2690

EP - 2737

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 6

ER -

ID: 331502175