Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Projective systemic modules   We develop the basic theory of projective modules and splitting in the more
general setting of systems. Systems provide a common language for most tropical
algebraic approaches including supertropical algebra, hyperrings (specifically
hyperfields), and fuzzy rings. This enables us to prove analogues of classical
theorems for tropical and hyperring theory in a unified way. In this context we
prove a Dual Basis Lemma and versions of Schanuel's Lemma.

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The categories of this paper are: quant-ph
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The categories of this paper are: cs
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph