Stable cohomology operation

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Definition

A stable cohomology operation of type $(\pi ,G)$ and of degree $k$ is defined as a set $\{{\theta }_n{\}}_{-\mathrm{\infty }}^{\mathrm{\infty }}$ of cohomology operations ${\theta }_n$ of type $(n,n+k,\pi ,G)$ such that ${\theta }_{n-1}$ is the cohomology suspension of ${\theta }_n$.

For a stable cohomology operation, all its constituent cohomology operations are group homomorphisms (this is not true for cohomology operations in isolation).