Nuclearity in the category of complete semilattices

AbstractIn a paper of the second author, a notion of nuclearity for the objects of an autonomous (or symmetric monoidal closed) category was introduced. In the present paper, the idea of nuclearity is extended to morphisms and the nature of the nuclear objects and morphisms in the category of complete join semilattices is determined. Our principal results are that the nuclear morphisms in this category coincide with the tight maps defined (essentially) by Raney and that the nuclear objects are precisely the completely distributive complete lattices