On reflective subcategories of locally presentable categories

Abstract

Are all subcategories of locally finitely presentable categories that are closed under limits and $\lambda$-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case $\lambda=\aleph_0$ the answer is affirmative also for all iso-full subcategories, \emph{i.\thinspace e.}, those containing with every pair of objects all isomorphisms between them. We discuss a possible generalization of this from $\aleph_0$ to an arbitrary $\lambda$.