The accessibility rank of weak equivalences

We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak equivalences between simplicial sets is finitely accessible.Comment: The main result is improved and its proof is simplified. To appear in Theory and Applications of Categories. 15 page

Locally class-presentable and class-accessible categories

We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the abstract homotopy theory

A generalization of Ohkawa's theorem

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.Comment: 13 pages; consequences in motivic homotopy theory have been adde

Limits of small functors

For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K*,V]. If K is large, its free completion under colimits is the V-category PK of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on PK.Comment: 17 page

Higher Order Containers

Abstract. Containers are a semantic way to talk about strictly positive types. In previous work it was shown that containers are closed under various constructions including products, coproducts, initial algebras and terminal coalgebras. In the present paper we show that, surprisingly, the category of containers is cartesian closed, giving rise to a full cartesian closed subcategory of endofunctors. The result has interesting applications syntax. We also show that while the category of containers has finite limits, it is not locally cartesian closed.

Dermacentor reticulatus: a vector on the rise

Dermacentor reticulatus is a hard tick species with extraordinary biological features. It has a high reproduction rate, a rapid developmental cycle, and is also able to overcome years of unfavourable conditions. Dermacentor reticulatus can survive under water for several months and is cold-hardy even compared to other tick species. It has a wide host range: over 60 different wild and domesticated hosts are known for the three active developmental stages. Its high adaptiveness gives an edge to this tick species as shown by new data on the emergence and establishment of D. reticulatus populations throughout Europe. The tick has been the research focus of a growing number of scientists, physicians and veterinarians. Within the Web of Science database, more than a fifth of the over 700 items published on this species between 1897 and 2015 appeared in the last three years (2013–2015). Here we attempt to synthesize current knowledge on the systematics, ecology, geographical distribution and recent spread of the species and to highlight the great spectrum of possible veterinary and public health threats it poses. Canine babesiosis caused by Babesia canis is a severe leading canine vector-borne disease in many endemic areas. Although less frequently than Ixodes ricinus, D. reticulatus adults bite humans and transmit several Rickettsia spp., Omsk haemorrhagic fever virus or Tick-borne encephalitis virus. We have not solely collected and reviewed the latest and fundamental scientific papers available in primary databases but also widened our scope to books, theses, conference papers and specialists colleagues’ experience where needed. Besides the dominant literature available in English, we also tried to access scientific literature in German, Russian and eastern European languages as well. We hope to inspire future research projects that are necessary to understand the basic life-cycle and ecology of this vector in order to understand and prevent disease threats. We conclude that although great strides have been made in our knowledge of the eco-epidemiology of this species, several gaps still need to be filled with basic research, targeting possible reservoir and vector roles and the key factors resulting in the observed geographical spread of D. reticulatus. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13071-016-1599-x) contains supplementary material, which is available to authorized users