Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The free tangent structure   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.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas