Abstract: Let S be a monoid, FGWI, WPF and STF denote the class of finitely generated weakly injective right S acts, weakly pullback flat right S acts and strongly torsion free right Sacts respectively. It is proved that if S is a left reversible monoid with a left zero, then every rightS actAi∈FGWI if and only if the coproduct ∪[DD(-*3]·[DD)]i∈IAi∈FGWI. IfS is a Noetherian monoid, then the directed colimit of fgweakly injective Sacts is fgweakly injective. At the same time, WPF covers and STF covers are investigated, the condition over which every right Sact has a FGWI cover is obtained. It is proved that every right Sact has a WPF cover over a finitely generated monoid with a finite geometric type and every right Sact has a STFcover over any monoid S.