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The appendix "A bestiary of 2–vector spaces" of Bartlett, Douglas, Schommer-Pries, Vicary, "Modular categories as representations of the 3-dimensional bordism 2-category" analyzes ...

For an $A_\infty$-category $\mathcal A$, one defines the group $K_0(\mathcal A)$ by $$K_0(\mathcal A) := \mathbb Z \operatorname{Ob} \operatorname{Tw} \mathcal A / \left<[A]+[B]-[C]\right>$$ ...

I currently am studying $A_{\infty}$-obstructions and to compute them I need to compute at least the $A_3$-data of an $\mathrm{Ext}$-algebra. More precisely, I have a functor $F:\mathcal{D}\left(X\...