Central groupoids are kind of neat but not that great

So, I have recently been reading/thinking a bit about central groupoids . This is a quite misnamed class of object; they're not groupoids, the term comes from an old use of "groupoid" to mean "magma". (Blech.) They're magmas (sets with a binary operation) satisfying the central identity, (ab)(bc)=b. You may recall my project regarding equational probabilities in algebraic structures . I…