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Forward Automatic Differentiation (AD) is a technique for augmenting programs to both perform their original calculation and also compute its directional derivative. The essence of Forward AD is to attach a derivative value to each number, and propagate these through the computation. When derivatives are nested, the distinct derivative calculations, and(More)
Assuming that B is a full A ∞-subcategory of a unital A ∞-category C we construct the quotient unital A ∞-category D ='C/B'. It represents the A u ∞-2-functor A → A u ∞ (C, A) mod B , which associates with a given unital A ∞-category A the A ∞-category of unital A ∞-functors C → A, whose restriction to B is contractible. Namely, there is a unital A(More)
For a differential graded k-quiver Q we define the free A ∞-category FQ generated by Q. The main result is that the restriction A ∞-functor A ∞ (FQ, A) → A 1 (Q, A) is an equivalence, where objects of the last A ∞-category are morphisms of differential graded k-quivers Q → A. A ∞-categories defined by Fukaya [Fuk93] and Kontsevich [Kon95] are(More)
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