The free tangent structure

Poon Leung

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arXiv · 1605.07275

The free tangent structure

Poon Leung

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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 this paper seeks to compare two of them: Synthetic Differential Geometry (SDG) and 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). SDG on the other hand is defined through the use of Weil algebras. The aim of this paper is to present a more precise relationship between the two approaches for describing tangent structures.

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Poon Leung. 2016-05-24. The free tangent structure. https://arxiv.org/abs/1605.07275

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