Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the universal coefficients formula for shape homology   In this paper it is investigated whether various shape homology theories
satisfy the Universal Coefficients Formula (UCF). It is proved that
pro-homology and strong homology satisfy UCF in the class FAB of finitely
generated abelian groups, while they do not satisfy UCF in the class AB of all
abelian groups. Two new shape homology theories (called UCF-balanced) are
constructed. It is proved that balanced pro-homology satisfies UCF in the class
AB, while balanced strong homology satisfies UCF only in the class FAB.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph