ScalingStacks

Lemma 9.47. The symmetric monoidal functor $\pi_{0}\colon\mathrm{Sp}_{\geq 0}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\mathrm{Ab}$ is right adjoint to the Eilenberg-MacLane spectrum functor $H$, which is lax symmetric monoidal. It induces a functor

$$\pi_{0}\colon\Cat_{\mathrm{Sp}_{\geq 0}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\Cat_{\mathrm{Ab}},$$

from categories enriched in connective symmetric spectra to categories enriched in abelian groups with right adjoint $H$.