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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 $A':=\{\{a\}\colon a\in A\}$?

(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.

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    $\begingroup$ Thanks for the pointer. Yes, discrete partition for $A\mapsto \{\{a\}\colon a\in A\}$ and indiscrete partition for $A\mapsto \{A\}$ appears the most sensible pair of technical terms for this, in tune with other usages in contemporary measure theory and topology. $\endgroup$
    – Peter Heinig
    Commented May 12, 2017 at 4:25

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$A'$ is the discrete partition of $A$.

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

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  • $\begingroup$ I believe the OP is after the name of the operation that sends a set to its discrete partition. $\endgroup$
    – Burak
    Commented May 11, 2017 at 19:39
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    $\begingroup$ Well the operation that sends a set to its power set is called "power set" I suppose, so the operation here would be "discrete partition". $\endgroup$
    – Bjørn Kjos-Hanssen
    Commented May 11, 2017 at 19:41
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    $\begingroup$ It's not just any partition, it's a very fine partition! :) $\endgroup$
    – Asaf Karagila ♦
    Commented May 11, 2017 at 21:42

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