8 citations · 21 across the 8 of their papers we have counts for
8 papers
Complicial structures in the nerves of omega-categories
Richard Steiner
It is known that strict omega-categories are equivalent through the nerve functor to complicial sets and to sets with complicial identities. It follows that complicial sets are equ…
The algebra of the nerves of omega-categories
Richard Steiner
We show that the nerve of a strict omega-category can be described algebraically as a simplicial set with additional operations subject to certain identities. The resulting structu…
Opetopes and chain complexes
Richard Steiner
We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike struc…
The algebraic structure of the universal complicial sets
Richard Steiner
The nerve of a strict omega-category is a simplicial set with additional structure, making it into a so-called complicial set, and strict omega-categories are in fact equivalent to…
Simple omega-categories and chain complexes
Richard Steiner
The category of strict omega-categories has an important full subcategory whose objects are the simple omega-categories freely generated by planar trees or by globular cardinals. W…
Thin fillers in the cubical nerves of omega-categories
Richard Steiner
It is shown that the cubical nerve of a strict omega-category is a sequence of sets with cubical face operations and distinguished subclasses of thin elements satisfying certain th…