Frobenius and the derived centers of algebraic theories

William G. Dwyer; Markus Szymik

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arXiv · 1410.3879

Frobenius and the derived centers of algebraic theories

William G. Dwyer·Markus Szymik

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Abstract

We show that the derived center of the category of simplicial algebras over every algebraic theory is homotopically discrete, with the abelian monoid of components isomorphic to the center of the category of discrete algebras. For example, in the case of commutative algebras in characteristic $p$, this center is freely generated by Frobenius. Our proof involves the calculation of homotopy coherent centers of categories of simplicial presheaves as well as of Bousfield localizations. Numerous other classes of examples are discussed.

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William G. Dwyer, Markus Szymik. 2014-10-14. Frobenius and the derived centers of algebraic theories. https://arxiv.org/abs/1410.3879

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