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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).
@article{TAC_2017_32_a8,
author = {Poon Leung},
title = {Classifying tangent structures using {Weil} algebras},
journal = {Theory and applications of categories},
pages = {286--337},
publisher = {mathdoc},
volume = {32},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a8/}
}
Poon Leung. Classifying tangent structures using Weil algebras. Theory and applications of categories, Tome 32 (2017), pp. 286-337. http://geodesic.mathdoc.fr/item/TAC_2017_32_a8/