Equivariant Topology and Derived Algebra

This volume contains eight research papers inspired by the 2019 'Equivariant Topology and Derived Algebra' conference, held at the Norwegian University of Science and Technology, Trondheim in honour of Professor J. P. C. Greenlees' 60th birthday. These papers, written by experts in the field, are intended to introduce complex topics from equivariant topology and derived algebra while also presenting novel research. As such this book is suitable for new researchers in the area and provides an excellent reference for established researchers. The inter-connected topics of the volume include: algebraic models for rational equivariant spectra; dualities and fracture theorems in chromatic homotopy theory; duality and stratification in tensor triangulated geometry; Mackey functors, Tambara functors and connections to axiomatic representation theory; homotopy limits and monoidal Bousfield localization of model categories.

An interpretation of dependent type theory in a model category of locally cartesian closed categories

Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the “gros” semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with the structure of a model of dependent type theory. The original interpretation in an individual lcc category can then be recovered by slicing. As in the original interpretation, we face the issue of coherence: Categorical structure is usually preserved by functors only up to isomorphism, whereas syntactic substitution commutes strictly with all type-theoretic structures. Our solution involves a suitable presentation of the higher category of lcc categories as model category. To that end, we construct a model category of lcc sketches, from which we obtain by the formalism of algebraically (co)fibrant objects model categories of strict lcc categories and then algebraically cofibrant strict lcc categories. The latter is our model of dependent type theory.

The nature of food promotions over one year in circulars from leading Belgian supermarket chains

Background To examine the proportion of healthier and less healthy food promotions in circulars of major Belgian supermarket chains. Methods Food promotions were collected from all circulars over 1 year from the five largest Belgian supermarket chains. Foods promoted were classified according to the World Health Organization Europe nutrient profile model categories and the level and purpose of processing as per the NOVA classification. In addition, promotional characters (i.e. cartoons, licensed characters, celebrities) and premium offers within the promotions were analysed. Results In total, 15,271 food promotions were analyzed. The most frequently promoted foods in circulars were processed meat, poultry and fish (11.8%); fresh and frozen fruit, vegetables and legumes (9.5%); soft drinks and sweetened beverages (9.0%); fresh and frozen meat, poultry, fish and eggs (8.6%); cakes, sweet biscuits and pastries (8.1%); ready-made and convenience foods (8.0%); chocolate and sugar confectionery; energy bars and sweet toppings (7.7%) and cheeses (5.7%). About 52.2% of food promotions across all circulars were for ultra-processed foods, with considerable variation across chains (42.9–61.6%). Promotional characters and premium offers were found within 5.3 and 19.5% of promotions respectively. For all chains, circular covers were healthier compared to entire circulars, with a lower proportion of ultra-processed foods and a higher proportion of fresh fruit and vegetables promoted. Conclusions Food promotions in circulars were most frequently for ultra-processed foods, with considerable variation across chains. Circular covers were healthier than entire circulars. Policies to reduce less healthy food promotions could contribute to improving the healthiness of supermarket food purchases.

Measuring Mental Model of Primary Teachers and Pre-service Teachers on Heat Transfer Concept

This study compares primary teachers' mental models with pre-service primary school teachers' mental models on the heat transfer concept. The mental model categories reviewed in this study include scientific, synthetic, and initial. This study's method was descriptive quantitative method, with research subjects 40 primary teachers and 40 pre-service primary teachers. This study's instrument is a conceptual understanding test consisting of three parts of a statement that asks for an explanation and description. The results showed that in understanding concepts test in synthetic mental models, 32.5%. In the category of initial mental models, there is a comparison of 32.5%. While in the concept of convection, there is a comparison of 2.5% in the scientific category. For synthetic mental models' category is 5%. In the category of initial mental models is 7.5%. For the concept of radiation, there is no comparison in the category of scientific mental models. Next there is a comparison of 7.5% in the category of synthetic mental models. In the category of initial mental models is 7.5%. Generally, elementary school teachers and students are in synthetic mental models and the initial mental models' category.