(r,t)-injectivity in the category S-Act

Abstract

In this paper, we show that injectivity with respect to the class D of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category well-behaves. Indeed, if M is a subclass of monomorphisms, M ∩ D-injectivity well-behaves. We also introduce the notion of (r, t)-injectivity in the category S-Act, where r and t are Hoehnke radicals, and discuss whether this kind of injectivity well-behaves.