A free algebra in the variety of groupoids. The free groupoid on a set of free generators coincides with the set of all bracketed words (cf. Word) in the elements of (each symbol is assumed to be taken in brackets, and the brackets are arranged so that each time only two brackets are multiplied out). The product of the words (a) and (b) is the word ((a)(b)).
Free groupoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Free_groupoid&oldid=16388