On free, projective, and strongly flat acts
The homological classification of monoids is considered. Theorem: All flat left S-acts (injective cogenerators, all cofree, all injective left S-acts) are strongly flat iff \(S=\{1\}\). Theorem: All projective generators in S-Act are free iff any eS, \(e^ 2=e\in S\), containing a left invertible element can be generated by a left invertible element. All terms have their usual categorical meaning, a left S-act M is called strongly flat if tensoring by M preserves equalizers and pullbacks.
scientific article; zbMATH DE number 3944157