  Let C be a small category and G be a tensor Grothendieck category. We define
a notion of atness in the category Fun(C; G) of all covariant functors from C
to G and show that the inclusion K(FlatA) ---> K(A) has a right adjoint where
K(A) is the homotopy category of A and K(FlatA) its subcategory consisting of
complexes of at functors. In addition, we find a replacement for the quotient
Dpac(FlatA) = K(FlatA)Kp(FlatA) of triangulated categories where Kp(FlatA) is
the homotopy category of all pure acyclic complexes of at functors.
