Let G:Ω→Ω′be a closed unital map between commutative,unital quantales. G induces a functor G from the category of Ω-categories to that of Ω′-categories.This paper is concerned with some basic properties of G.Th...Let G:Ω→Ω′be a closed unital map between commutative,unital quantales. G induces a functor G from the category of Ω-categories to that of Ω′-categories.This paper is concerned with some basic properties of G.The main results are:(1) when Ω,Ω′are integral,G:Ω→Ω′and F:Ω′→Ωare closed unital maps,F is a left adjoint of G if and only if F is a left adjoint of G;(2) G is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for G to preserve completeness in the sense that GA is a complete Ω′-category whenever A is a complete Ω-category.展开更多
基金the National Natural Science Foundation of China (No.10771147)the Program for New Century Excellent Talents in University (No.05-0779)
文摘Let G:Ω→Ω′be a closed unital map between commutative,unital quantales. G induces a functor G from the category of Ω-categories to that of Ω′-categories.This paper is concerned with some basic properties of G.The main results are:(1) when Ω,Ω′are integral,G:Ω→Ω′and F:Ω′→Ωare closed unital maps,F is a left adjoint of G if and only if F is a left adjoint of G;(2) G is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for G to preserve completeness in the sense that GA is a complete Ω′-category whenever A is a complete Ω-category.
