The M[--] and --[M] functors and five short lemma in $H_v$-modules

Authors: YASER VAZIRI, MANSOUR GHADIRI, BIJAN DAVVAZ

Abstract: The largest class of multivalued systems satisfying the module-like axioms are the $H_v$-modules. The main tools concerning the class of $H_v$-modules with the ordinary modules are the fundamental relations. Based on the relation $\varepsilon^*$, exact sequences in $H_v$-modules are defined. In this paper, we introduce the $H_v$-module $M[A]$ and determine its heart and the connection between equivalence relations $\varepsilon^*_{M[A]}$ and $\varepsilon^*_A$. Moreover, we define the $M[-]$ and $-[M]$ functors and investigate the exactness and some concepts related to them. Finally, we prove the five short lemma in $H_v$-modules.

Keywords: $H_v$-module, exact sequence, five short lemma, weak equality, fundamental relation $\varepsilon^*$

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