Hi all Note my new e-mail. I had to get a new e-mail to exclude html. I am not an expert on oo-categories but i am sure there is a structure to the "class" of all omega-categories. I hope all this will not depend on the definition of an oo-category. 6> Is the "class" of oo-categories of a certain recursive depth always an oo-category of depth one higher than the previous depth? I think yes for both strict and weak oo-categories. What should the "class" of all n-categories in Makkais foundation be called to describe it technically accurately? An oo-cosmos? in the categorical sense of a cosmos. I am not sure but this "class" maby also contain all oo-categories. Are there different strict/weak n-categories with n any infinite ordinal number omega? omega does remind of an ordinal number. The category need not to be accessible by forming categories of categories, just satisfy some axioms of an strict/weak oo-category for oo=omega. There might be a better definition of an omega-category if it is necessary at all, i don't know. Best regards Rafael Borowiecki [For admin and other information see: http://www.mta.ca/~cat-dist/ ]