Commuting properties of Ext. (Q2861581)

In the present paper the author studies various commuting properties for \(\mathrm{Ext}\) covariant, respectively contravariant, functors defined on Abelian groups. Let \(\mathcal C\) be a class of Abelian groups. An Abelian group \(G\) is called \(\mathcal C\)-Ext-small if \(\mathrm{Ext}(G,-)\) preserves direct sums from \(\mathcal C\), respectively \(G\) is called \(\mathcal C\)-Ext-slender if \(\mathrm{Ext}(-,G)\) inverts products from \(\mathcal C\). In the main results of the paper the author characterizes Abelian groups \(G\) which are \(\mathcal C\)-Ext-small (slender) for various classes \(\mathcal C\).