Definition 4.9.12.  Let u ∈ ℕ, R be a ring. We define:
RModu(R) := [RMod(R)(Hom(A, B))A,B ∈ RMod(R)(idC)C ∈ RMod(R)(∘)D,E,F ∈ RMod(R)]u is a/an u-small category
Remarks.

The objects of this category are actually isomorphism classes of modules.

References.