Re: Terminology of locally small categories without replacement

Dear Jean,

Could you please tell me: (i) Given a category S how does one chose the finitely complete 2- category K and the class C of small objects so that the locally small objects of K in your sense, are the locally small fibrations over S ?

Take K = Fib(S) and take C to be the representable fibrations. For me this is actually the easiest way to remember the definition of locally small fibration.

(iii) What significant mathematical examples can you give of your notion ?

See (i). Best regards, Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]