ScalingStacks

Definition 2.7. A spectral functor $F\colon{\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}$ is called

• •

  a triangulated equivalence if the induced functor

  $$F_{!}^{\cf}\colon\widehat{{\mathcal{A}}}_{\tri}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}\widehat{{\mathcal{B}}}_{\tri}$$

  is a DK-equivalence of spectral categories.

• •

  a Morita equivalence if the induced functor

  $$F_{!}^{\cf}\colon\widehat{{\mathcal{A}}}_{\perf}\longrightarrow\widehat{{\mathcal{B}}}_{\perf}$$

  is a DK-equivalence of spectral categories.