Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Universal Equivalence of Groups under Free Constructions   In 1971 J. Stallings introduced a generalisation of amalgamated products of
groups -- called a pregroup, which is a particular kind of a partial group. He
defined the universal group U(P) of a pregroup P to be a universal object (in
the sense of category theory) extending the partial operations on P to group
operations on U(P). This turns out to be a versatile and convenient
generalisation of classical group constructions: HNN-extensions and amalgamated
products. In this respect the following general question arises. Which
properties of pregroups, or relations between pregroups, carry over to the
respective universal groups? In this paper it is proved that universal
equivalence of pregroups extends to universal equivalence of universal groups.
Applications to free products with amalgamation and HNN-extensions are then
described.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org