• Corpus ID: 207870019

Opetopic algebras I: Algebraic structures on opetopic sets

@article{Thanh2019OpetopicAI,
  title={Opetopic algebras I: Algebraic structures on opetopic sets},
  author={C{\'e}dric Ho Thanh and Chaitanya Leena Subramaniam},
  journal={arXiv: Category Theory},
  year={2019}
}
We define a family of structures called ``opetopic algebras'', which are algebraic structures with an underlying opetopic set. Examples of such are categories, planar operads, and Loday's combinads over planar trees. Opetopic algebras can be defined in two ways, either as the algebras of a ``free pasting diagram'' parametric right adjoint monad, or as models of a small projective sketch over the category of opetopes. We define an opetopic nerve functor that fully embeds each category of… 
Opetopic algebras III: Presheaf models of homotopy-coherent opetopic algebras
For Λ the category of free opetopic algebras, we construct a model structure a la Cisinski on the category of presheaves over Λ, and show that is is equivalent to opetopic complete Segal spaces. This
The incidence comodule bialgebra of the Baez–Dolan construction

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