Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Another approach to the Kan-Quillen model structure   By careful analysis of the comparison map from a simplicial set to its image
under Kan's ex-infinity functor we obtain a new and combinatorial proof that it
is a weak homotopy equivalence. Moreover, we obtain a presentation of it as a
strong anodyne extension. From this description we are able to quickly deduce
some basic facts about ex-infinity and hence provide a new construction of the
Kan-Quillen model structure on simplicial sets, which avoids the use of
topological spaces or minimal fibrations.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph