  Enriched versions of type A Schubert polynomials are constructed with
coefficients in a polynomial ring in variables $c_1, c_2, \ldots$. Specializing
these variables to $0$ recovers the double Schubert polynomials of Lascoux and
Sch\"utzenberger; specializing them to certain power series recovers the
back-stable double Schubert polynomials of Lam, Lee, and Shimozono;
specializing them to Schur Q-polynomials relates them to the type C double
Schubert polynomials of Ikeda, Mihalcea, and Naruse. Many formulas for
classical Schubert polynomials generalize to this setting. They give, and are
characterized by, formulas for degeneracy loci.
