Connective complex K-theory spectrum

Definition 9.4.2. We denote by \[ \BUP := (\Vect (\pt )^{\simeq })^{\grp } \qin \CGrp (\An ) \] the group completion of \(\Vect (\pt )^{\simeq }\) with respect to direct sum, using the left adjoint \((-)^{\grp }\) from Corollary 5.4.5. We define the connective complex K-theory spectrum \(\ku \in \Sp _{\geq 0}\) to be the connective spectrum corresponding to \(\BUP \) under the equivalence \(\Sp _{\geq 0} \simeq \CGrp (\An )\) of Theorem 5.4.6.