Holmstrom Cohomology operation

Consider two Generalized cohomology theories $h$ and $k$ on CW pairs. A sequence of natural transformations $\Psi^n: h^n \to k^{n+s}$ commuting with the connecting homomorphisms is called a natural transformation of degree $s$. If $h = k$, call this a stable cohomology operation of degree $s$. There is a similar notion for Reduced cohomology theories.

Book: Cohomology Operations and Applications in Homotopy Theory, by Mosher and Tangora

nLab page on Cohomology operation