http://ncatlab.org/nlab/show/compact+object+in+an+(infinity,1)-category
http://ncatlab.org/nlab/show/small+object
I think, but may be completely wrong, that compact would mean constructible for sheaves of sets, and perfect for complexes of abelian sheaves. In motivic homotopy theory, I believe that suspension spectra of smooth schemes are compact.
MO questions with several nice answers and a link to an nLab summary: http://mathoverflow.net/questions/59282/sums-compact-objects-f-g-objects-in-categories-of-modules
nLab page on Compact object