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 $lambda$.
Download