Geodesic
On the commutative algebra of categories
Berman, John1
1 Department of Mathematics, University of Virginia, Charlottesville, VA, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2963-3012

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 ∞–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.

DOI : 10.2140/agt.2018.18.2963
Classification : 18C10, 55U40, 13C60, 19D23
Keywords: higher algebra, Lawvere theory, operad

Berman, John 1

1 Department of Mathematics, University of Virginia, Charlottesville, VA, United States 
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Berman, John. On the commutative algebra of categories. Algebraic and Geometric Topology, Tome 18 (2018) no. 5, pp. 2963-3012. doi: 10.2140/agt.2018.18.2963

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