Orientals as free weak ω\omega-categories

The orientals are the free strict $\omega$-categories on the simplices introduced by Street. The aim of this paper is to show that they are also the free weak $\omega$-categories on the same generating data. More precisely, we exhibit the Street nerves of the orientals as fibrant replacements of the simplices in Verity's model structure for complicial sets.Comment: v2: 24 pages. Major revision. Published versio

Weakly invertible cells in a weak ω\omega-category

We study weakly invertible cells in weak $\omega$-categories in the sense of Leinster, adopting Cheng's coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $\omega$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $\omega$-categories to weak $\omega$-categories, and show that every weak $\omega$-category has a largest weak $\omega$-subgroupoid.Comment: 21 pages. Comments welcome

Equivalence of cubical and simplicial approaches to (∞,n)(\infty,n)-categories

We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for ($n$-trivial, saturated) comical sets to the category of marked simplicial set equipped with a model structure for ($n$-trivial, saturated) complicial sets is a Quillen equivalence. Our proof is based on the theory of cones, previously developed by the first two authors together with Lindsey and Sattler.Comment: 60 pages; v2 improvements to expositio

Inactivation of Vibrio vulnificus hemolysin through mutation of the N- or C-terminus of the lectin-like domain

Vibrio vulnificus is an etiological agent causing serious systemic infections in the immunocompromised humans or cultured eels. This species commonly produces a hemolytic toxin consisting of the cytolysin domain and the lectin-like domain. For hemolysis, the lectin-like domain specifically binds to cholesterol in the erythrocyte membrane, and to form a hollow oligomer, the toxin is subsequently assembled on the membrane. The cytolysin domain is essential for the process to form the oligomer. Three-dimensional structure model revealed that two domains connected linearly and the C-terminus was located near to the joint of the domains. Insertion of amino acid residues between two domains was found to cause inactivation of the toxin. In the C-terminus, deletion, substitution or addition of an amino acid residue also elicited reduction of the activity. However, the cholesterol-binding ability was not affected by the mutations. These results suggest that mutation of the C- or N-terminus of the lectin-like domain may result in blockage of the toxin assembly