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We introduce a notion of total acyclicity associated to a subcategory of an abelian category and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius category, whose induced stable category is equivalent to the homotopy category of totally acyclic complexes. Applied to the flat--cotorsion theory over a coherent ring, this provides a new description of the category of cotorsion Gorenstein flat modules; one that puts it on equal footing with the category of Gorenstein projective modules.

Homotopy categories of totally acyclic complexes with applications to the flat–cotorsion theory