  We outline a definition of accessible and presentable objects in a 2-category
$\mathcal K$ endowed with a "KZ context", that is to say a pair of
lax-idempotent monads interacting in a prescribed way; this perspective
suggests a unified treatment of many "Gabriel-Ulmer like" theorems, asserting
how presentable objects arise as reflections of generating ones. We outline the
notion of "(Gabriel-Ulmer) envelope" for a KZ context, sufficient to concoct
Gabriel-Ulmer duality. We end the paper with a roundup of examples, involving
classical (set-based and enriched), low dimensional category theory, and a
perspective for future work, rooted in higher category theory and homotopy
theory.
