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It seems that some people use the term "anti-Leibniz order" for what I'd call the "diagrammatic order" of composition: writing $f;g$ for the composition of $f$ and $g$ instead of $g\circ f$.

(I have no intention to discuss which order is "better"; I use both depending on context. Also, I believe the confusion is due to the fact that we forgot to mirror decimal numbers when we copied the concept from Arabic. For a reference to "anti-Leibniz", see https://ncatlab.org/nlab/show/anafunctor.)

Now, where does that terminology come from, and what does Leibniz have to do with it?

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  • $\begingroup$ Is it possible that the terminology comes from ncatlab? It's also used at ncatlab.org/nlab/show/composition where reference is made to "the notation introduced by the followers of Leibniz for composition of functions." $\endgroup$
    – Gerry Myerson
    Jun 2, 2020 at 12:59
  • $\begingroup$ Oh, I'd overlooked that one, thank you. Now, do people use "anti-Leibniz" outside of ncatlab? $\endgroup$
    – Uli Fahrenberg
    Jun 2, 2020 at 14:12
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    $\begingroup$ I am pretty close to the "inside" of ncatlab, and have never heard this name. I would call it "French". $\endgroup$
    – Theo Johnson-Freyd
    Jun 2, 2020 at 22:57
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    $\begingroup$ Or, sometimes, "reverse Polish". $\endgroup$
    – Theo Johnson-Freyd
    Jun 2, 2020 at 22:58

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