ScalingStacks

Definition 2.1. A spectral functor $F:{\mathcal{A}}\mathchoice{\longrightarrow}{\rightarrow}{\rightarrow}{\rightarrow}{\mathcal{B}}$ is a DK-equivalence, if:

• •

  for all objects $x,y\in{\mathcal{A}}$, the morphism in $\mathcal{S}$

  $$F(x,y):{\mathcal{A}}(x,y)\longrightarrow{\mathcal{B}}(Fx,Fy)$$

  is a stable equivalence and

• •

  the induced functor

  $$[F]:[{\mathcal{A}}]\longrightarrow[{\mathcal{B}}]$$

  is an equivalence of categories.