Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Very good homogeneous functors in manifold calculus   Let M be a smooth manifold, and let O(M) be the poset of open subsets of M.
Let C be a category that has a zero object and all small limits. A homogeneous
functor (in the sense of manifold calculus) of degree k from O(M) to C is
called very good if it sends isotopy equivalences to isomorphisms. In this
paper we show that the category VGHF of such functors is equivalent to the
category of contravariant functors from the fundamental groupoid of Conf(k, M)
to C, where Conf(k, M) stands for the unordered configuration space of k points
in M. As a consequence of this result, we show that the category VGHF is
equivalent to the category of representations of the fundamental group of
Conf(k, M) in C, provided that Conf(k, M) is connected. We also introduce a
subcategory of vector bundles that we call very good vector bundles, and we
show that it is abelian, and equivalent to a certain category of very good
functors.

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The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom