On strongly flat and \(\Omega\)-Mittag-Leffler objects in the category \(((R\mathrm{-mod})^{\mathrm{op}},\mathrm{Ab})\). (Q1949839)

Let \(R\) be ring, \(R\)-mod the category of finitely presented left \(R\)-modules and \(((R\mathrm{-mod})^{\mathrm{op}},\mathrm{Ab})\) the category of contravariant additive functors, where \(\mathrm{Ab}\) denotes the category of Abelian groups. The author introduces the notion of strongly flat and \(\Omega\)-Mittag-Leffler functors extending the module case. In Section 3, characterizations of both classes of functors, using tensor products of functors, are obtained. In the last section, it is shown that the class of strongly flat functors is closed under extensions, direct sums and pure subfactors and the class of \(\Omega\)-Mittag-Leffler functors is closed under extensions, finite direct sums and pure subfactors. Moreover, conditions for the classes being closed under direct products are studied.