Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-585311Special Issue Dedicated to Prof. George A. Grätzer20190701(r,t)-injectivity in the category $S$-Act1691967660110.29252/cgasa.11.1.169ENMahdieh HaddadiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.Seyed Mojtaba Naser SheykholislamiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.Journal Article20180305In 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.https://cgasa.sbu.ac.ir/article_76601_35b108e0967457882abe5232f68aa727.pdf