This paper continues the development of a simplicial theory of weak ω-categories, by studying categories which are enriched in weak complicial sets. These complicial Gray-categories generalise both the Kan complex enriched categories of homotopy theory and the 3-categorical Gray-categories of weak 3-category theory. We derive a simplicial nerve construction, which is closely related to Cordier ...

This paper proposes to define a weak higher-dimensional category to be a simplicial set satisfying properties. The definition is a refinement of that suggested at the end of [St3] which required extra structure on the simplicial set. The paper [St3] constructed the simplicial nerve of a (strict) ω-category. The principal aim of the paper was to prove that the construction was right adjoint to t...

The orientals are the free strict ω-categories on simplices introduced by Street. aim of this paper is to show that they also weak same generating data. More precisely, we exhibit complicial nerves as fibrant replacements in Verity's model structure for sets.