The category of Colombeau algebras

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 Colombeaus 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.