-tuple and -tuple of Covariant Functors

A right A-module M is a -module provided that M is self-small and any exact sequence

0 → N → L → Q → 0,

with L, Q ∈ Stat(M) remains exact after applying the functor HomA(M, -) if and only if N ∈ Stat(M). A right A-module M is called a -module if it is self-small, (n + 1)-quasi-projective and n-Pres(M) = (n + 1)-Pres(M). In this work we generalize the concepts of -module and -modules to the concepts of -tuple and -tuple of Contravariant Functors between abelian categories.