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arXiv · 1606.05606

On the Commutative Algebra of Categories

John D. Berman
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Abstract

We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be recovered in this way as categories of modules over a commutative semiring category (or $\infty$-category in the last case). This language provides a simultaneous generalization of the formalism of algebraic theories (operads, PROPs, Lawvere theories) and stable homotopy theory, with essentially a variant of algebraic K-theory bridging between the two.

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John D. Berman. 2016-06-17. On the Commutative Algebra of Categories. https://doi.org/10.2140/agt.2018.18.2963

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