Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The homotopy relation in a category with weak equivalences   We define a homotopy relation between arrows of a category with weak
equivalences, and give a condition under which the quotient by the homotopy
relation yields the homotopy category. In the case of the fibrant-cofibrant
objects of a model category this condition holds, and we show that our notion
of homotopy coincides with the classical one. We also show that Quillen's
construction of the homotopy category of a model category, in which the arrows
are homotopical classes of a single arrow between fibrant-cofibrant objects,
can be made as well for categories with weak equivalences using this notion of
homotopy. We deduce from our work the saturation of model categories. The
proofs of these results, which consider only the weak equivalences, become
simpler (as it is usually the case) than those who involve the whole structure
of a model category.

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The categories of this paper are: cond-mat
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The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: physics