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.

  • 10
    $\begingroup$ 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. $\endgroup$ Mar 12, 2021 at 20:54
  • 14
    $\begingroup$ Of course the horizontal categorification of monoid is category and not monoidoid :) $\endgroup$ Mar 12, 2021 at 20:55
  • 9
    $\begingroup$ Ellipsoids, paraboloids and hyperboloids have been around for a long time. $\endgroup$ Mar 12, 2021 at 21:03
  • 8
    $\begingroup$ 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
    Mar 12, 2021 at 22:20
  • 27
    $\begingroup$ Perhaps this is more appropriate for Mathoid Overflow. It's not really a math question... $\endgroup$ Mar 12, 2021 at 22:37

2 Answers 2


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.

  • 5
    $\begingroup$ (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
    Mar 12, 2021 at 21:03
  • 1
    $\begingroup$ Also, purely mathematically, a groupoid is not a quasi-group, I think. :-) $\endgroup$
    – LSpice
    Mar 12, 2021 at 21:03
  • 10
    $\begingroup$ On the other hand, the empty set (which can be described by the word v-oid) is relatively recent. $\endgroup$ Mar 12, 2021 at 23:50
  • 4
    $\begingroup$ @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...” $\endgroup$ Mar 13, 2021 at 9:57
  • 3
    $\begingroup$ This suggests that Nicomedes is the right answer to the question, since he was the one who first talked about conchoids. $\endgroup$
    – Matt F.
    Mar 14, 2021 at 6:23

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.