%0 Journal Article %T (r,t)-injectivity in the category $S$-Act %J Categories and General Algebraic Structures with Applications %I Shahid Beheshti University %Z 2345-5853 %A Haddadi, Mahdieh %A Naser Sheykholislami, Seyed Mojtaba %D 2019 %\ 07/01/2019 %V 11 %N Special Issue Dedicated to Prof. George A. Grätzer %P 169-196 %! (r,t)-injectivity in the category $S$-Act %K Injectivity %K $S$-act %K Hoehnke radical %R 10.29252/cgasa.11.1.169 %X 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. %U https://cgasa.sbu.ac.ir/article_76601_35b108e0967457882abe5232f68aa727.pdf