We study the class of modules, called cosilting modules, which are defined as the categorical duals of silting modules. Several characterizations of these modules and connections with silting modules are presented. We prove that Bazzoni's theorem about the pure-injectivity of cotilting modules is also valid for cosilting modules.
Communicated by J. TrlifajThe notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we show that to every cosilting module could be associated a particular t-structure in the derived module category.
In this paper we consider a pair of right adjoint contravariant functors between abelian categories and describe a family of dualities induced by them.
Abstract. Starting with a pair F : A B : G of additive contravariant functors which are adjoint on the right, between abelian categories, and with a class U, we define the notion of (F, U)-coplex. Considering a reflexive object U of A with F(U ) = V projective object in B, we construct a natural duality between the category of all (F, add(U ))-coplexes in A and the subcategory of B consisting in all objects in B which admit a projective resolution with all terms in the class add(V ).Mathematics Subject Classification (2010): 16E30, 16D90.
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