ScalingStacks

Definition 4.18. Let $\mathcal{C}$ be an additive category. The split Grothendieck group of $\mathcal{C}$ is defined as:

$$K_{0}(\mathcal{C}):=\frac{\mathrm{Span}_{\mathbb{Z}}\{\text{isomorphism classes }[x]\text{ of objects in }\mathcal{C}\}}{([x\oplus y]=[x]+[y]\mid x,y\in\mathrm{Ob}(\mathcal{C}))}$$