Weakly tilting bimodules (Q2753154)

The classical definition of a tilting module \(T\) (of projective dimension one) allows to identify the category of modules generated by \(T\) with a kernel of an \(\text{Ext}^1\)-functor and cogenerated modules with the kernel of a \(\text{Tor}_1\)-functor. The present article defines more general `weakly tilting bimodules' by replacing these equalities by inclusions (of the generated or cogenerated modules into the respective kernels). Many classical results such as the Brenner-Butler theorem have analogues in this setup. Related results can be found in another article by \textit{A. Tonolo} [J. Algebra 232, No. 1, 282-298 (2000; Zbl 0967.16003)].