小瓢虫传媒

Logic from the enriched categorical point of view

In logic, regular theories are those whose axioms are built using only equations, relation symbols, conjunctions, and existential quantification. The categories of models of such theories have been widely studied and characterised in purely category theoretical terms through the notions of exact and abielian category, and of injectivity class; I will recall these during the talk.

When moving to the context of categories enriched over a base V, corresponding notions of "exact V-category" and "V-injectivity class" have been studied by several authors, but no enriched notion of regular logic was considered in the literature before. The aim of this talk, which is based on joint work with Rosicky, is to fill this gap by introducing a notion of "enriched regular logic" that interacts well with the category theoretical counterparts mentioned above. Among others, we'll see examples from the additive, differentially graded, and 2-categorical setting.