Injectivity in the category of measurable S-acts

Abstract

In this paper, we define measurable [Formula: see text]-acts on monoids and construct a new category, namely Meas Act-[Formula: see text]. We investigate the behavior of this category with respect to product, coproduct, pushout, pullback, equalizer and coequalizer. Next, we study the injectivity and complete injectivity in category Meas Act-[Formula: see text] and show any measurable [Formula: see text]-act can be embedded into complete injectivity. Moreover, we investigate the Skornjakov’ theorem for measurable S-acts.