On equalizer-flat and pullback-flat acts
Let S be a monoid. A left S-act A is said to be equalizer-flat (pullback- flat) if the functor -\(\otimes A: Act\)-S\(\to Ens\) preserves equalizers (resp. pullbacks). Denote with (P) the following property of a left S-act A: if \(sa=tb\) for s,t\(\in S\) and a,b\(\in A\), then there are elements u,v\(\in S\) and \(a_ 1\in A\) such that \(su=tv\), \(ua_ 1=a\) and \(va_ 1=b\). It is shown that all equalizer-flat, pullback-flat acts or acts having property (P), are flat. All S-acts are pullback-flat (equalizer- flat) iff \(S=\{1\}\) \((S=\{1\}\) or \(S=\{0,1\})\). All S-acts have property (P) iff S is a group.
scientific article; zbMATH DE number 4015023