In this paper, we discuss the structure of intuitionistic fuzzy (IF) homomorphisms, exact sequences and some other concepts in category of IF modules. We study on IF exact sequences and IF Hom functors in IFR – Mod and obtain some results about them. If R is a commutative ring and \(\bar{0}\rightarrow A\mathop \to \limits^{\tilde f}B\mathop \to \limits^{\tilde g}C\) is an exact sequence in IFR – Mod, where \({\tilde f}\) is IF split homomorphism, then we show that HomIF – R (D,–) preserves the sequence for every D ∈ IFR – Mod. Also IF projective modules will be introduced and investigated in this paper. Finally we define product and coproduct of IF modules and show that if M is an R-module, A = (μA, νA) ≤IFM and ei ∈ E(R) for any i ∈ I, then
\(Hom({\mathop \coprod \limits_{i \in I} 0_{{{{\mathop{Re}\nolimits}}_i}}^{IF},A}) \cong \mathop \prod \limits_{i \in I} Hom({0_{{{{\mathop{Re}\nolimits}}_{i}}}^{IF},A}).\)
