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There are lots of structures which have name suffixed by "oid". Off the top of my head, matroid, greedoid, perfectoid, causaloid...

Who started this? AFAIK, "matroid", by Whitney, was a start, and led the way to several combinatorial oids. However, the Cardioid has had its name for some centuries now, so the use of the suffix is old.

Still, it seems a bit different to name a family of specific objects, and to name some sort of abstract structure.

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    $\begingroup$ The only consistent use of the -oid suffix I know is for Horizontal categorication (ncatlab.org/nlab/show/horizontal+categorification), so typically, groupoid, algebroid, ringoid, etc... in which case the origin is definitely the name "groupoid". But it is unclear if all the examples you mention fit into this picture ? Otherwise the use of -oid to name "something vaguely ressembling something else" does not strike me as really being a fashion nor being specific to mathematics. $\endgroup$
    – Simon Henry
    Commented Mar 12, 2021 at 20:54
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    $\begingroup$ Of course the horizontal categorification of monoid is category and not monoidoid :) $\endgroup$
    – Benjamin Steinberg
    Commented Mar 12, 2021 at 20:55
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    $\begingroup$ Ellipsoids, paraboloids and hyperboloids have been around for a long time. $\endgroup$
    – Michael Renardy
    Commented Mar 12, 2021 at 21:03
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    $\begingroup$ At the first place the suffix -oid is not mathematical (dictionnaire.exionnaire.com/que-signifie.php?mot=-oide). My favorite mathematical one anyway, in French, is patatoïde, one of the most important geometric shapes in the whole history. $\endgroup$
    – YCor
    Commented Mar 12, 2021 at 22:20
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    $\begingroup$ Perhaps this is more appropriate for Mathoid Overflow. It's not really a math question... $\endgroup$
    – Donu Arapura
    Commented Mar 12, 2021 at 22:37

2 Answers 2

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The suffix "-oid" means the same as "quasi", so "resembling", "like". A groupoid is a quasi-group, like a group. There are hundreds of words in that category, covering many scientific disciplines.

In the "early use of mathematical words" database I find:

250 BC: conchoid
200 BC: cissoid
400: trapezoid
1650: trochoid
1672: ellipsoid
1685: cochleoid
1830: epicycloid
1836: paraboloid
1837: strophoid
1844: centroid
1872: geoid, gyroid
1878: nephroid
1879: deltoid
1881: prismatoid
1891: cuboid
1935: matroid

The Woid on-Oid by William Safire comments on the proliferation of -oids:

We all know that the use of -oid to create a noun has been growing by leapoids and bounds. Among the earliest were android, or "automaton in human form," created in 1727, and asteroid, "small body like a star," in 1802. Scientists and mathematicians were especially attracted to the ending, juggling their cylindroids, globoids and spheroids.

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    $\begingroup$ (I took '-oid' out of math mode; I hope that was OK.) I wouldn't have expected cuboid to be so late! The first ones that occurred to me were ellipsoid and spheroid; I wonder (but not enough to check) when they first occurred. $\endgroup$
    – LSpice
    Commented Mar 12, 2021 at 21:03
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    $\begingroup$ Also, purely mathematically, a groupoid is not a quasi-group, I think. :-) $\endgroup$
    – LSpice
    Commented Mar 12, 2021 at 21:03
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    $\begingroup$ On the other hand, the empty set (which can be described by the word v-oid) is relatively recent. $\endgroup$
    – Michael Renardy
    Commented Mar 12, 2021 at 23:50
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    $\begingroup$ @ArnaldoMandel No, as already commented by Benjamin Steinberg that distinction may belong to groupoid (Brandt, 12 Dec 1925, p. 361): “Eine solche Menge miteinander verknüpfte Elemente soll Gruppoid heißen, wenn...” $\endgroup$
    – Francois Ziegler
    Commented Mar 13, 2021 at 9:57
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    $\begingroup$ This suggests that Nicomedes is the right answer to the question, since he was the one who first talked about conchoids. $\endgroup$
    – user44143
    Commented Mar 14, 2021 at 6:23
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Though this might not be what you are expecting, I will explain you "oidification" or horizontal categorification as I understood (Experts are fell free to add or edit as necessary). This is the process that generalizes a "certain type of category with a single object" to "such type of categories with multiple objects". This is done mostly via "enriching" the initial category $\mathcal{C}$ over another monoidal category $\mathcal{K},$ which roughly says homsets (set of arrows two objects) of $\mathcal{C}$ are replaced by objects of $\mathcal{K}.$

Examples include

X X-oid Enrichment
monoid Category categories enriched over Set
Category 2-Category categories enriched over Cat
Group Groupoid
Ring Ringoid category enriched in tensor category Ab
Quantale Quantaloid category enriched in suplattices
Algebr Algebroid category enriched in Vect or RMod
C*-algebra C*-category *-category enriched in Ban

You can find more details ringoid, and algebroid here. But as far as I know Hopf algebroids and Lie algebroids does not fit into this general definition of algebroids, but still multi-object generalizations of their counterparts.

Also, it should worth remind that not every enrichment of a categories consider as an "odification". For example (Lawvere) generalized metric spaces is a category enriched in the monoidal poset category $([0,\infty],\ge),$ where the monoidal product is taken to be addition.

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    $\begingroup$ when will we see a categoroid? $\endgroup$
    – Manfred Weis
    Commented Mar 14, 2021 at 12:35
  • $\begingroup$ @ManfredWeis It already happened. $\endgroup$
    – Francois Ziegler
    Commented Mar 14, 2021 at 22:41

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