2016/03/30 by Enxin Wu, Wu, Enxin
Computer Science · Mathematics · #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Theory of Mathematics #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1603.09266
openalex publication_date 2016/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we use some basic quasi-topos theory to study two functors: one adding infinitesimals of Fermat reals to diffeological spaces (which generalize smooth manifolds including singular spaces and infinite dimensional spaces), and the other deleting infinitesimals on Fermat spaces. We study the properties of these functors, and calculate some examples. These serve as fundamentals for developing differential geometry on diffeological spaces using infinitesimals in a future paper.