The category of Colombeau algebras
Lorenzo Luperi Baglini, Paolo Giordano

TL;DR
This paper explores the categorical properties of Colombeau AG-algebras, a unified framework that generalizes many existing Colombeau algebras, and examines their implications for solving generalized ODEs.
Contribution
It analyzes the categorical aspects of Colombeau AG-algebras and demonstrates their impact on the solvability of generalized ordinary differential equations.
Findings
Colombeau AG-algebras unify various Colombeau constructions.
Categorical properties influence the solvability of generalized ODEs.
The framework generalizes multiple existing Colombeau algebras.
Abstract
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 , the full one , the NSA based algebra of asymptotic functions , and the diffeomorphism invariant algebras , and . 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.
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