  Making use of Freyd's free abelian category on a preadditive category we show
that if $T:D\rightarrow \mathcal{A}$ is a representation of a quiver $D$ in an
abelian category $\mathcal{A}$ then there is an abelian category $\mathcal{A}
(T)$, a faithful exact functor $F_T: \mathcal{A} (T) \to \mathcal{A}$ and an
induced representation $\tilde T: D \to \mathcal{A} (T)$ such that $F_T\tilde
T= T$ universally. We then can show that $\mathbb{T}$-motives as well as Nori's
motives are given by a certain category of functors on definable categories.
