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We show that the (positive) zoom complexes, here called tree complexes, with fairly natural morphisms, form a dual category to the category of positive opetopes with contraction epimorphisms. We also show how this duality can be slightly generalized to thicket complexes and opetopic cardinals.
We show that the category of positive opetopes with contraction morphisms, i.e. all face maps and some degeneracies, forms a test category. The category of positive opetopic sets pOpeSet can be defined as a full subcategory of the category of polyg
The aim of this sequel to arXiv:1812.02935 is to set up the cornerstones of Koszul duality and Koszulity in the context of a large class of operadic categories. In particular, we will prove that operads, in the generalized sense of Batanin-Markl, gov
Let $R$ be a commutative noetherian ring with a semi-dualizing module $C$. The Auslander categories with respect to $C$ are related through Foxby equivalence: $xymatrix@C=50pt{mathcal {A}_C(R) ar@<0.4ex>[r]^{Cotimes^{mathbf{L}}_{R} -} & mathcal {B}_C
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 constructio