Terminology for objects whose co-Yoneda functor commutes with sifted colimits – mathoverflow.net
John Pardon
Given an object $c$ of a category $\mathsf C$, we say that:
$c$ is small when $\mathrm{Hom}_{\mathsf C}(c,-)$ commutes with $\kappa$-filtered colimits for some cardinal $\kappa$.
$c$ is compact when ...