A note on the diamond operator

We show that if $1{\le }_{W}F$ and $F\star F{\le }_{W}F$, then $F^\diamond \leq_W F$,where$\star$and$\diamond$ are the following operations in the Weihrauch lattice: $\star$ is the compositional product, which allows the use of two principles in sequence, while the diamond operator $\diamond$ allows an arbitrary but finite number of uses of the given principle in sequence. This answers a question of Pauly.