Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homology groups of cubical sets   The paper is devoted to homology groups of cubical sets with coefficients in
contravariant systems of Abelian groups. The study is based on the proof of the
assertion that the homology groups of the category of cubes with coefficients
in the diagram of Abelian groups are isomorphic to the homology groups of
normalized complex of the cubical Abelian group corresponding to this diagram.
The main result shows that the homology groups of a cubical set with
coefficients in a contravariant system of Abelian groups are isomorphic to the
values of left derived functors of the colimit functor on this contravariant
system. This is used to obtain the isomorphism criterion for homology groups of
cubical sets with coefficients in contravariant systems, and also to construct
spectral sequences for the covering of a cubical set and for a morphism between
cubical sets.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom