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If $f \circ g \circ f = f$ and $g \circ f \circ g = g$, $f$ and $g$ are functions, is there a name for $(f, g)$?

stralep
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1 Answers1

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I have heard them called quasi-inverses.

Arthur
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  • To add to this, if $f$ is a quasi-inverse of $g$, then $g$ isn't necessarily a quasi-inverse of $f$, so the OP's requirement is slightly more strict. – Théophile Mar 07 '19 at 15:11
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    @Théophile I would say that "$f$ and $g$ are quasi-inverses of one another" gets around this. But certainly, you're right, "is a quasi-inverse of" is not a symmetric relation. – Arthur Mar 07 '19 at 15:17