Cartesian closed stable categories

Authors:
Ni Liu;Sheng-Gang Li
Affiliations:
College of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi'an, China;College of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi'an, China
Venue:
Information Sciences—Informatics and Computer Science: An International Journal
Year:
2005

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Abstract

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 bc-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.