A note on the Penon definition of nn-category

We show that doubly degenerate Penon tricategories give symmetric rather than braided monoidal categories. We prove that Penon tricategories cannot give all tricategories, but we show that a slightly modified version of the definition rectifies the situation. We give the modified definition, using non-reflexive rather than reflexive globular sets, and show that the problem with doubly degenerate tricategories does not arise.Comment: 14 pages, to appear in Cahiers de Topologie et Geometrie Differentielle Categorique

Bindings as bounded natural functors

We present a general framework for specifying and reasoning about syntax with bindings. Abstract binder types are modeled using a universe of functors on sets, subject to a number of operations that can be used to construct complex binding patterns and binding-aware datatypes, including non-well-founded and infinitely branching types, in a modular fashion. Despite not committing to any syntactic format, the framework is “concrete” enough to provide definitions of the fundamental operators on terms (free variables, alpha-equivalence, and capture-avoiding substitution) and reasoning and definition principles. This work is compatible with classical higher-order logic and has been formalized in the proof assistant Isabelle/HOL

The blameworthiness of health and safety rule violations

Man-made disasters usually lead to the tightening of safety regulations, because rule breaking is seen as a major cause of them. This reaction is based on the presumptions that the safety rules are good and that the rule-breakers are wrong. The reasons the personnel of a coke factory gave for breaking rules raise doubt about the tenability of these presumptions. It is unlikely that this result would have been achieved on the basis of a disaster evaluation or High-Reliability Theory. In both approaches, knowledge of the consequences of human conduct hinders an unprejudiced judgement about the blameworthiness of rule breaking