The logic of structures (Q1196790)

``Proof-theoretic'' properties of various categories of accessible categories (Cartesian closure, normal forms, links with linear logic) are investigated. The connection of accessible categories with sketches is used (accessible categories being the categories of models of a small sketch). The author works in ZFC + the axiom of universes. The following topics are studied in detail: \(\beta\)-accessible categories and \(\beta\)- continuous functors (with a regular cardinal); Cartesian closed categories of accessible categories; some linear features (in the sense of Girard's linear logic) of the theory of \(\alpha\)-presentable categories.