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A free algebra in the variety of groupoids. The free groupoid on a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041560/f0415601.png" /> of free generators coincides with the set of all bracketed words (cf. [[Word|Word]]) in the elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/f/f041/f041560/f0415602.png" /> (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)).