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

(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.

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.