Connective cover of a spectrum

Corollary 5.4.7. The inclusion \(\Sp _{\geq 0} \hookrightarrow \Sp \) admits a right adjoint \(\tau _{\geq 0}\colon \Sp \to \Sp _{\geq 0}\) given by \(\tau _{\geq 0}(X) = \bB ^{\infty }\bOmega ^{\infty }X\). □