2025/11/22 by Taho, Masaki
Computer Science · Mathematics · #57P05 (Primary) #58A05 (Secondary) #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2511.17871
openalex publication_date 2025/11/22 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28
We study tangent spaces in the setting of diffeological spaces. Several distinct tangent functors have been introduced, each of which extends the classical tangent functor from smooth manifolds. In this paper, we construct infinitely many non-isomorphic tangent functors on diffeological spaces. We compare our constructions with existing models, including the internal and external tangent spaces. Our results show that the choice of tangent functor is far from unique outside smooth manifolds.