Are the finite dimensional comodules the compact objects in the category of comodules over a Hopf algebra? If yes, is there a reference? If no, which are the compact objects? Here by compact I mean that the Hom functor from the compact object preserves filtered colimits. Thank you!

  • $\begingroup$ I believe this is true over a field, at least, and that it follows from the fact that every comodule is a filtered colimit of finite-dimensional comodules. $\endgroup$ – Qiaochu Yuan Oct 24 '15 at 18:08
  • $\begingroup$ Thank you! How would you prove this? Is there a natural right adjoint to the Hom functor in this case? $\endgroup$ – m.pap Oct 24 '15 at 20:58

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