Localisations of locally presentable categories. II (Q917678)

This is a continuation of Part I [ibid. 58, No.3, 227-233 (1989; Zbl 0677.18009)]. However, it does not deal with enriched categories; the authors content themselves to consider localizations E of categories \(A=Lex(C^{op},Set)\). They show how E arises as Lex Sh\({}_ J(C)\) for a Grothendieck topology on C. Moreover, they give twelve good structural aspects of C and show how they transfer to A. For instance, if C is an elementary topos, then A is a locally finitely presentable Grothendieck topos and the Yoneda embedding y: \(C\to A\) is a fully faithfull logical morphism.