Infinitely Many Tangent Functors on Diffeological Spaces

TL;DR

This paper demonstrates the existence of infinitely many distinct tangent functors on diffeological spaces, highlighting the non-uniqueness of tangent space constructions beyond smooth manifolds.

Contribution

It constructs infinitely many non-isomorphic tangent functors on diffeological spaces and compares them with existing models, expanding understanding of tangent structures.

Findings

Existence of infinitely many tangent functors

Comparison with internal and external tangent spaces

Non-uniqueness of tangent functors outside manifolds

Abstract

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.