Mantese, Francesca; Tonolo, Alberto Natural dualities. (English) Zbl 1069.16011 Algebr. Represent. Theory 7, No. 1, 43-52 (2004). Summary: Let \(S\) be an arbitrary associative ring and \(_SW\) be a left \(S\)-module. Denote by \(R\) the ring \(\text{End}_SW\) and by \(\Delta\) both the contravariant functors \(\operatorname{Hom}_S(-,W)\) and \(\operatorname{Hom}_R(-,W)\). A module \(M\) is reflexive if the evaluation map \(\delta_M\colon M\to\Delta^2M\) is an isomorphism. Any direct summand of finite direct sums of copies of \(_SW\) and \(R_R\) is reflexive. Increasing in a minimal way the classes of reflexive modules, a “cotilting condition” on finitely generated \(R\)-modules naturally arises. Cited in 1 ReviewCited in 3 Documents MSC: 16E30 Homological functors on modules (Tor, Ext, etc.) in associative algebras 16D90 Module categories in associative algebras Keywords:Morita dualities; cotilting modules; reflexive modules; contravariant functors; direct summands; finitely generated modules PDFBibTeX XMLCite \textit{F. Mantese} and \textit{A. Tonolo}, Algebr. Represent. Theory 7, No. 1, 43--52 (2004; Zbl 1069.16011) Full Text: DOI