Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Universal Property of Derived Manifolds   It is well known that any model for derived manifolds must form a higher
category. In this paper, we propose a universal property for this higher
category, classifying it up to equivalence. Namely, the $\infty$-category
$\mathbf{DMfd}$ of derived manifolds has finite limits, is idempotent complete,
and receives a functor from the category of manifolds which preserves
transverse pullbacks and the terminal object, and moreover is universal with
respect to these properties. We then show this universal property is equivalent
to another one, intimately linking the $\infty$-category of derived manifolds
to the theory of $C^\infty$-rings. More precisely, $\mathbb{R}$ is a
$C^\infty$-ring object in $\mathbf{DMfd}$, and the pair
$\left(\mathbf{DMfd},\mathbb{R}\right)$ is universal among idempotent complete
$\infty$-categories with finite limits and a $C^\infty$-ring object. We then
show that (a slight extension beyond the quasi-smooth setting of) Spivak's
original model satisfies our universal property.

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg