Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A relationship between multiple conjugation quandle/biquandle colorings   We define a functor $\mathcal{Q}$ from the category of multiple conjugation
biquandles to that of multiple conjugation quandles. We show that for any
multiple conjugation biquandle $X$, there is a one-to-one correspondence
between the set of $X$-colorings and that of $\mathcal{Q}(X)$-colorings
diagrammatically for any handlebody-link and spatial trivalent graph. In
particular, we prove that the set of $G$-family of Alexander biquandles
colorings is isomorphic to that of $G$-family of Alexander quandles colorings
as modules.

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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas