Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compositions and tensor products of linear maps between matrix algebras   We exhibit an identity which connects tensor products and compositions of
linear maps between matrix algebras through the Choi matrices. As applications
of this identity, we characterize mapping cones in terms of tensor products,
provide several equivalent statements to PPT (positive partial transpose)
square conjecture in terms of tensor products, and show that the Choi matrix
may be defined independent of coordinates to some extent. We also consider
various mapping cones arising from ampliation and factorization.

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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: math
27
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: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol