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

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

Keywords:

Injectivity , S-act , Hoehnke radical