inspired by conversations with quillen, segal soon introduced another approach to constructing algebraic "k"-theory under the name of γ-objects. segal's approach is a homotopy analog of grothendieck's construction of "k". where grothendieck worked with isomorphism classes of bundles, segal worked with the bundles themselves and used isomorphisms of the bundles as part of his data. this results in a spectrum whose homotopy groups are the higher "k"-groups (including "k"). however, segal's approach was only able to impose relations for split exact sequences, not general exact sequences. in the category of projective modules over a ring, every short exact sequence splits, and so γ-objects could be used to define the "k"-theory of a ring. however, there are non-split short exact sequences in the category of vector bundles on a variety and in the category of all modules over a ring, so segal's approach did not apply to all cases of interest.