## Abstract

At the heart of differential geometry is the construction of the tangent bundle of a manifold. There are various abstractions of this construction, and of particular interest here is that of Tangent Structures. Tangent Structure is defined via giving an underlying category M and a tangent functor T along with a list of natural transformations satisfying a set of axioms, then detailing the behaviour of T in the category End(M). However, this axiomatic definition at first seems somewhat disjoint from other approaches in differential geometry. The aim of this paper is to present a perspective that addresses this issue. More specifically, this paper highlights a very explicit relationship between the axiomatic definition of Tangent Structure and the Weil algebras (which have a well established place in differential geometry).

Original language | English |
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Pages (from-to) | 286-337 |

Number of pages | 52 |

Journal | Theory and Applications of Categories |

Volume | 32 |

Issue number | 9 |

Publication status | Published - 15 Feb 2017 |

## Keywords

- tangent structure
- Weil algebra