Coherence for bicategorical cartesian closed structure

We prove a strictification theorem for cartesian closed bicategories. First, we adapt Power’s proof of coherence for bicategories with finite bilimits to show that every bicategory with bicategorical cartesian closed structure is biequivalent to a 2-category with 2-categorical cartesian closed structure. Then we show how to extend this result to a Mac Lane-style “all pasting diagrams commute” coherence theorem: precisely, we show that in the free cartesian closed bicategory on a graph, there is at most one 2-cell between any parallel pair of 1-cells. The argument we employ is reminiscent of that used by Čubrić, Dybjer, and Scott to show normalisation for the simply-typed lambda calculus (Čubrić et al., 1998). The main results first appeared in a conference paper (Fiore and Saville, 2020) but for reasons of space many details are omitted there; here we provide the full development.

Treatment management between orthodontists and general practitioners performing clear aligner therapy

ABSTRACTObjective:To investigate differences in case selection, treatment management, and aligner treatment expertise between orthodontists and general practitioners.Materials and Methods:A parallel pair of original surveys with three sections (case selection, treatment management, and demographics) was sent to orthodontists (N = 1000) and general dentists (N = 1000) who were providers of aligner treatment.Results:Orthodontists had treated significantly more patients with aligners, had treated more patients with aligners in the previous 12 months, and had received more aligner training than general dentists (P < .0001). In general, case confidence increased with increasing experience for both orthodontists and general dentists. After adjusting for experience, there was a significant difference in aligner case confidence between orthodontists and general dentists for several malocclusions. General dentists were more confident than orthodontists in treating deep bite, severe crowding, and Class II malocclusions with aligners (P ≤ .0001). Significant differences were also found for all treatment management techniques except interproximal reduction.Conclusion:There was a significant difference in case selection, treatment management, and aligner expertise between orthodontists and general dentists, although the differences in case selection were small. Overall, it was shown that orthodontists and general dentists elected to treat a variety of moderate to severe malocclusions with aligners but with different utilization of recommended auxiliaries, perhaps demonstrating a difference in treatment goals.