Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the classification of fibrations   Classification questions are often about understanding components of a
category. It is much more desirable however to be able to understand the entire
homotopy type of this category and not just the set of its components. In this
paper we prove that this is possible for the category of functors indexed a
small category I which assign to any morphism in I a weak equivalence in a
given model category. We identify the homotopy type of this category with the
mapping space out of the nerve of I into the classifying space of the space of
weak equivalences of values of these functors. We use it to reprove the
classical classification of fibration theorem of Stasheff and its
generalizations by Dwyer-Kan.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph