Hi, In [1], Mike Shulman explains how one can define: * the category of magmas as an inserter in the 2-category of (large) categories, * the category of semigroups as an equifier, * and so on up to the category of rings. Can we go further? What is the 2-categorical limit to be used in order to define the category of small categories? But since small categories form a 2-category, maybe I should reformulate my question: What is the 3-categorical limit to be used in order to define the 2-category of small categories? While I am asking... What is the (n+2)-categorical limit to be used in order to define the (n+1)-category of n-categories? what is the omega-categorical limit to be used in order to define the omega-category of omega-categories? [1] http://mathoverflow.net/questions/9269/category-of-categories-as-a-foundatio... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]