  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.
