PULLBACKS AND FLATNESS PROPERTIES OF ACTS. I

Let S be a monoid. A right S-act A is pullback flat ( = strongly flat) if the functor A ⊗ – (from the category of left S-acts to the category of sets) preserves pullbacks. We investigate possible general-izations of this notion, obtained either by restricting attention to cer-tain types of pullbacks or by weakening the requirement of pullback preservation. We note that it is possible to describe the already familiar notions of flatness, (principal) weak flatness, and torsion freeness in these terms. Furthermore, a number of new properties arise