Classifying tangent structures using Weil algebras

Poon Leung*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    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 languageEnglish
    Pages (from-to)286-337
    Number of pages52
    JournalTheory and Applications of Categories
    Issue number9
    Publication statusPublished - 15 Feb 2017


    • tangent structure
    • Weil algebra


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