Accessible categories with a class of limits

In this paper we characterize those accessible V-categories that have limits of a specified class. We do by introducing the notion companion C for class weights Ψ, as collection special types colimit diagrams are compatible with Ψ. then Ψ-limits accessibly embedded and C-virtually reflective in presheaf V-category, C-models sketches. This allows us to recover standard theorems locally presentable, multipresentable, polypresentable categories instances same general framework. addition, our theorem covers case any weakly sound provides new perspective on presentable categories.