Abstract:
In this work we study the relations between the closure operators of two module categories connected by two adjoint contravariant functors. The present article is a continuation of the paper [1] (Part I), where the same question is investigated in the case of two adjoint covariant functors.
An arbitrary bimodule $_RU_S$ defines a pair of adjoint contravariant functors $H_1=Hom_R(\text{-},U)\colon R\text{-}\mathrm{Mod}\to\mathrm{Mod}\text{-}S$ and $H_2=Hom_S(\text{-},U)\colon\mathrm{Mod}\text{-}S\to R\text{-}\mathrm{Mod}$ with two associated natural transformations and . In this situation we study the connections between the closure operators of the categories $R\text{-}\mathrm{Mod}$ and $\mathrm{Mod}\text{-}S$.
Keywords and phrases:category of modules, closure operator, adjoint functors, contravariant functor.
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