# Can the objects of every concrete category themselves be realized as small categories?

More precisely, is every concrete category C isomorphic to a category C' of small categories such that the morphisms between two elements of C are precisely the functors between their images in C'?

At some point I started adopting this point of view as a philosophy without ever bothering to actually verify it.

• Isomorphic or equivalent? And equivalent or (weak) equivalent-as-2-categories? Oct 19 '09 at 6:41