I thought that I had encountered this word somewhere, probably in the nLab, until I discovered that I can't find it anywhere on the internet; now I'm wondering if I somehow confabulated it. I was under the impression that category theorists occasionally refer to the dual of some concept (or just any concept with "co" attached to its name) as a coconcept. (I also thought I might have seen it in Ross Street's Quantum Groups, but I can't find it there either; nor with a Google Books search.)

  • $\begingroup$ I'm not sure I understand the question (is it about the prefix "co" or the literal word "coconcept"?) but people have been asking about the prefix "co-" on the internet for abput 20 years at least: mta.ca/~cat-dist/catlist/1999/co-prefix $\endgroup$ – Mark S. Mar 14 '17 at 18:01
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    $\begingroup$ Have you tried searching for the term "ncept"? $\endgroup$ – Jeremy Rickard Mar 14 '17 at 18:02
  • $\begingroup$ @MarkS. The literal word. But that discussion you linked is fascinating. $\endgroup$ – Archelon Mar 14 '17 at 19:33
  • $\begingroup$ @JeremyRickard: An excellent thought. I hadn't. Unfortunately such a search proved unilluminating (although I did learn that "sex is the best way to summon spirits"). $\endgroup$ – Archelon Mar 14 '17 at 19:36

In categories in which the distributive law doesn't hold, the use of 'sum' for that construction is often avoided; it is instead called 'coproduct,' which means (as mentioned in the last session) 'dual of product.' One of the fundamental ways in which one category differs from another is the relation between the concepts and the coconcepts. In many categories the distributive law is valid, but in other categories there are instead quite different, but equally interesting, relationships between product and coproduct.

Lawvere, Schanuel. Conceptual mathematics: A first introduction to categories. p. 276

This is the only occurrence of the word "coconcept" in mathematics literature (other than the index of that same book) that I was able to find through google.

  • $\begingroup$ The reason being, presumably, that the concept of concept is self-dual, so that while a given concept has a co-concept, there's no difference intrinsically between the two notions. $\endgroup$ – Kevin Carlson Mar 14 '17 at 19:04
  • $\begingroup$ This is definitely where I saw it. Should have thought to look there. (But apparently Google found it for you; I wonder why not for me?) I'll wait a bit and see if anyone has any other examples before I accept this as the answer, but such it is. $\endgroup$ – Archelon Mar 14 '17 at 19:39
  • $\begingroup$ @KevinCarlson: Thus I would expect the term 'coconcept' (or 'ncept') to be used only in constructions (or, equivalently, nstructions) where it has a clearly specified relatum. $\endgroup$ – Archelon Mar 14 '17 at 19:44

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