  In [11], we introduced the notion of asymptotic gauge (AG), and we used it to
construct Colombeau AG-algebras. This construction concurrently generalizes
that of many different algebras used in Colombeau's theory, e.g. the special
one $\mathcal{G}^{\srm}$, the full one $\gse$, the NSA based algebra of
asymptotic functions $\hat{\mathcal{G}}$, and the diffeomorphism invariant
algebras $\gsd$, $\mathcal{G}^{2}$ and $\hat{\mathcal{G}}$. In this paper we
study the categorical properties of the construction of Colombeau AG-algebras
with respect to the choice of the AG, and we show their consequences regarding
the solvability of generalized ODE.
