ScalingStacks

Definition 5.8. For an $\mathcal{F}$-algebra $A$ in $\mathcal{M}$, we define the $\mathcal{F}$-Hochschild cohomology

$$\hh^{*}_{\mathcal{F}}(A)={\mathcal{H}om}_{\mathrm{Mod}_{A}^{\mathcal{F}}}(A,A)$$

to be the object of $\mathcal{M}$ representing the endomorphisms of $A$ as an object of $\mathrm{Mod}_{A}^{\mathcal{F}}(\mathcal{M})$.