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.Comment: 40 page