The algebras of stable operations and cooperations in derived Witt theory with
rational coefficients are computed and an additive description of cooperations in
derived Witt theory is given. The answer is parallel to the well-known case of
K-theory of real vector bundles in topology. In particular, we show that stable
operations in derived Witt theory with rational coefficients are given by the values on
the powers of the Bott element.
