The equivalence between many-to-one polygraphs and opetopic sets

Cédric Ho Thanh 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
Inria de Paris, CNRS - Centre National de la Recherche Scientifique, UPD7 - Université Paris Diderot - Paris 7, PPS - Preuves, Programmes et Systèmes
Abstract : From the polynomial approach to the definition of opetopes of Kock et al., we derive a category of opetopes, and show that its set-valued presheaves, or opetopic sets, are equivalent to many-to-one polygraphs. As an immediate corollary, we establish that opetopic sets are equivalent to multitopic sets, introduced and studied by Harnick et al, and we also address an open question of Henry.
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Contributor : Cédric Ho Thanh <>
Submitted on : Thursday, December 6, 2018 - 2:40:18 PM
Last modification on : Friday, April 19, 2019 - 4:55:24 PM
Long-term archiving on : Thursday, March 7, 2019 - 1:36:58 PM


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  • HAL Id : hal-01946918, version 1
  • ARXIV : 1806.08645



Cédric Ho Thanh. The equivalence between many-to-one polygraphs and opetopic sets. 2018. ⟨hal-01946918⟩



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