The words "category" and "monad" existed already in philosophy. The usage of the terms in category theory seems to be slightly influenced by the philosophical meaning, but actually the concepts are by far not the same.

In particular, Lawvere reconciled the two notions of category much later, and the philosophical notion of monad seems rather more related to the homonymous concept in non-standard analysis.

So, why did Eilenberg and Mac Lane choose the name "category", out of many possible, what's the story?

And who and why choose the term "monad", for the monads of category theory? (I guess that comes from "monoid", but is it true?)

Any reference on these mathematical etymologies would be also highly appreciated.

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    $\begingroup$ This EnglishSE question english.stackexchange.com/questions/30654/… about monads could be interesting. $\endgroup$ – Arnaud D. Jan 9 at 18:32
  • $\begingroup$ As for "categories", I've always thought it was referring to the idea that you have several things (here the objects) you are working with, as with the elements of "groups" or "sets" (I believe "rings" also follow this idea, but it got lost in translation). $\endgroup$ – Arnaud D. Jan 9 at 18:40
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    $\begingroup$ You can find a few sentences about in the notes after the first chapter of Mac Lane's Categories for Working Mathematician. $\endgroup$ – Ilya Vlasov Jan 9 at 18:43

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