ScalingStacks

For a family of objects $\mathcal{T}$ in an idempotent-closed additive category $\mathcal{C}$ we consider the locally unital algebra with the distinguished idempotents $e_{M}=\operatorname{id}_{M}$ for $M\in\mathcal{T}$

(2.2)

$\displaystyle\operatorname{End}_{\mathcal{C}}(\mathcal{T})=\bigoplus_{M,N\in\mathcal{T}}\operatorname{Hom}_{\mathcal{C}}(M,N).$