Complexes of Gorenstein Flat Modules and Gorenstein Cotorsion Modules

A complex (C, δ) is called strongly Gorenstein flat if C is exact and Ker δ ⁿ is Gorenstein flat in R-Mod for all n ∈ ?. Let 𝒮𝒢 stand for the class of strongly Gorenstein flat complexes. We show that a complex C of left R-modules over a right coherent ring R is in the right orthogonal class of 𝒮𝒢 if and only if C ⁿ is Gorenstein cotorsion in R-Mod for all n ∈ ? and Hom^.(G, C) is exact for any strongly Gorenstein flat complex G. Furthermore, a bounded below complex C over a right coherent ring R is in the right orthogonal class of 𝒮𝒢 if and only if C ⁿ is Gorenstein cotorsion in R-Mod for all n ∈ ?. Finally, strongly Gorenstein flat covers and 𝒮𝒢^⊥-envelopes of complexes are considered. For a right coherent ring R, we show that every bounded below complex has a 𝒮𝒢^⊥-envelope.