What is a standard technical term in axiomatic set theory for the operation which sends a given set $A$ to the set $A':=\{\{a\}\colon a\in A\}$?

(Replacement implies that $A'$ is a set.)

Some pointers to relevant places in the literature would also be appreciated, especially if (0) the treatments emphasize large infinite sets and (1) take a point of view on this operation within a larger theoretical context, possibly characterizing it as an endofunctor of $\textsf{Sets}$ having certain properties. (It appears, though it is not the motivation for this question, that $A=\emptyset$ is its only fixed point.)

In case of epistemic answers being in short supply, deontic answers giving opinions how this operation ought to be called and denoted are also appreciated.