We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it while also having a purely in-tensional interpretation of the identity types. On the other hand, those conditions are… (More)
We explore the possibility and some potential payoffs of using the theory of accessible categories in the study of categories of logics. We illustrate this by two case studies focusing on the category of finitary structural logics and its subcategory of algebraizable logics.
We observe that the splitting of a given logic L into sublogics Li can be seen as a covering of L by the Li in a category of logics and take the first steps in exploring the possibility of applying the related language of Grothendieck topologies in this setting.