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



Usual technical term for replacing a set by the set of singletons of its members?
$A'$ is the [discrete partition](https://math.stackexchange.com/questions/153276/a-formal-name-for-smallest-and-largest-partition) of $A$.


That is, we think of it as a partition of $A$ induced by the finest equivalence relation, the identity relation.


