Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the homotopy theory of $\mathbf{G}$ - spaces   The aim of this paper is to show that the most elementary homotopy theory of
$\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over
$\mathbf{BG}$, where $\mathbf{G}$ is a fixed group. Both homotopy theories are
presented as Relative categories. We establish the equivalence by constructing
a strict homotopy equivalence between the two relative categories. No Model
category structure is assumed on either Relative Category.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ