Hi, Batanin, Leinster and other have presented related definitions of weak n-groupoid in terms of contractible globular operads. I personally find these definitions of "contractible n-groupoids" extremely beautiful. I am interested to learn what evidence we have that the homotopy hypothesis might be true for (at least one of) these definitions. Some good evidence is provided by Peter LeFanu Lumsdaine's [1] proof that a homotopy type gives rise to an infinity-groupoid in the sense of Leinster. There is other work along similar lines. But, as far as I am aware, it remains possible that contractible n-groupoids might in general be weaker structures than homotopy n-types. A fun way to investigate this would be to verify small instances of phenomena associated to the periodic table in contractible n-groupoids. For example, Christoph Dorn has shown me a proof that the Eckmann-Hilton argument holds in a Leinster 2-category; that is, for an object X, and for 2-morphisms f,g:id[X]-->id[X], we have f.g=g.f, thereby establishing one of the first phenomena predicted by the periodic table. Have any higher phenomena from the periodic table been verified? Or, is there other evidence that contractible n-groupoids behave "homotopically" in general? Best wishes, Jamie [1] http://peterlefanulumsdaine.com/research/Lumsdaine-Weak-omega-cats-from-ITT-... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]