We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak ω-categories, showing that the universal and canonical cofibrant replacement of the operad for strict ω-categories is precisely Leinster's operad for weak ω-categories.
Copyright  Cambridge Philosophical Society. Published by Cambridge University Press. Article originally published in [Garner R. "A Homotopy-theoretic universal property of Leinster's operad for weak ω-categories." Math. Proc. Camb. Phil. Soc. (2009), 147, 615]. The original article can be found at [http://dx.doi.org/10.1017/S030500410900259X].