Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model Categories and Simplicial Methods   There are many ways to present model categories, each with a different point
of view. Here we'd like to treat model categories as a way to build and control
resolutions. This an historical approach, as in his original and spectacular
applications of model categories, Quillen used this technology as a way to
construct resolutions in non-abelian settings; for example, in his work on the
homology of commutative algebras, it was important to be very flexible with the
notion of a free resolution of a commutative algebra. Similar issues arose in
the paper on rational homotopy theory. (This paper is the first place where the
now-traditional axioms of a model category are enunciated.) We're going to
emphasize the analog of projective resolutions, simply because these are the
sort of resolutions most people see first. Of course, the theory is completely
flexible and can work with injective resolutions as well.

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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio