most recent 30 from http://mathoverflow.net 2013-05-22T02:42:00Z http://mathoverflow.net/feeds/question/22152 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22152/finitely-related-objects-in-categories Michel Hebert 2010-04-22T05:36:27Z 2010-04-22T05:36:27Z

<p>Is anyone aware of some work mentioning a plausible categorical definition of "finitely related" object ? I mean an intrinsic one, which does not depend on some forgetful functor.</p> <p>(I am aware that even in algebraic categories, there cannot be one which fits with the classical definition - independent of a given forgetful functor- because even free objects are not preserved by categorical equivalences.I am also aware of Paul Taylor's suggestion in his CUP 1999's Practical Foundations (Exercises VII 23-24), however we discussed this and he agrees that his Exercise 24 seems incorrect: there he defines a finitely related object X in <em>C</em> as one for which <em>C</em>(X,-) preserves filtered colimits of strong epis, but this is really too strong (infinite sets do not satisfy in Set), and is not equivalent to his definition in Exercise 23.)</p>