Cartesian closed stable categories
The aim of this paper is to establish some Cartesian closed categories which are between the two Cartesian closed categories: SLP (the category of L-domains and stable functions) and DI (the full subcategory of SLP whose objects are all dI-domains). First we show that the exponentials of every full subcategory of SLP are exactly the spaces of stable functions. Then we prove that the full subcategories SDMBC, SDCBC and SDABC of SLP which contain DI are all Cartesian closed, where the objects of SDMBC (resp., SDCBC, SDABC) are all distributive be-domains which are meet-continuous (resp., continuous, algebraic). We also obtain many non-Cartesian closed full subcategories of SLP and present some reflective relations between those categories concerned. (C) 2004 Elsevier Inc. All rights reserved.
cartesian closed category stable functions stable orders bc-domains reflective subcategory