Abstract: Among various features of algebraic K-theory, there is known to be covariance with respect to finite flat morphisms of schemes. In this talk we will see, in which sense K-theory is universal as a cohomology theory with such covariance. Time permitting, we will discuss an analogous universality property for hermitian K-theory. This is joint work with Marc Hoyois, Joachim Jelisiejew, Denis Nardin, and Burt Totaro.