The following question looks so natural that somebody's bound to have looked into it: Does the functor Cat^op ---> CAT A |--> [A,Set] reflect isomorphisms (more generally: limits)? related questions (i.e. ones that would solve the problem or at least help solving it) are -- Are epimorphisms in Cat those functors F:A-->B for which F[A] generates B by composites and inverses of isomorphisms (in B)? -- is the source of all covariant hom-functors an extremal mono-source in CAT? The answers are probably in the literature - but where? Thanks a lot, Lutz Schroeder -- ----------------------------------------------------------------------------- Lutz Schroeder Phone +49-421-218-4683 Dept. of Computer Science Fax +49-421-218-3550 University of Bremen lschrode@informatik.uni-bremen.de P.O.Box 330440, D-28334 Bremen http://www.informatik.uni-bremen.de/~lschrode -----------------------------------------------------------------------------