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

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The largest class of multivalued systems satisfying the module-like axioms are the Hv-modules. The main tools concerning the class of Hv-modules with the ordinary modules are the fundamental relations. Based on the relation , exact sequences in Hv-modules are dened. In this paper, we introduce the Hv-module M(A) and determine its heart and the connection between equivalence relations M(A) and A. Moreover, we dene the M( ) and (M) functors and investigate the exactness and some concepts related to them. Finally, we prove the ve short lemma in Hv-modules.