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.)
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.