  We define higher Frobenius-Schur indicators for objects in linear pivotal
monoidal categories. We prove that they are category invariants, and take
values in the cyclotomic integers. We also define a family of natural
endomorphisms of the identity endofunctor on a $k$-linear semisimple rigid
monoidal category, which we call the Frobenius-Schur endomorphisms. For a
$k$-linear semisimple pivotal monoidal category -- where both notions are
defined --, the Frobenius-Schur indicators can be computed as traces of the
Frobenius-Schur endomorphisms.
