Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model category of diffeological spaces   The existence of a model structure on the category $\mathcal{D}$ of
diffeological spaces is crucial to developing smooth homotopy theory. We
construct a compactly generated model structure on the category $\mathcal{D}$
whose weak equivalences are just smooth maps inducing isomorphisms on smooth
homotopy groups. The essential part of our construction of the model structure
on $\mathcal{D}$ is to introduce diffeologies on the sets $\Delta^{p}$ $(p \geq
0)$ such that $\Delta^{p}$ contains the $k^{th}$ horn $\Lambda^{p}_{k}$ as a
smooth deformation retract.

19
The categories of this paper are: eess
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ