Locally presentable categories are considered as the "glorified", i.e. categorical, version of algebraic lattices. They can be characterized as full reflective subcategories of presheaf toposes where the embedding preserves cofiltered colimits (i.e. are Scott continuous) which is in accordance with the fact that every algebraic lattice arises as the image of a complete prime algebraic lattice (down closed subsets of a poset order by subset inclusion) under a Scott continuous closure operator. So far so good. But in Makkai and Par'e's book it is shown that every Grothendieck topos is in particular locally presentable. However, one easily sees that the posetal analogue doesn't hold. Grothendieck toposes arise as localizations of presheaf toposes. However, localizations of complete prime algebraic lattices are precisely the frames, i.e. cHa's, which need not be algebraic lattices. Has anyone give a good intuitive reason why the analogy breaks? Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]