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- Oleksandr Manzyuk
- Electr. Notes Theor. Comput. Sci.
- 2012

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)

We prove that the 2-category of closed categories of Eilenberg and Kelly is equivalent to a suitable full 2-subcategory of the 2-category of closed multicategories.

- UNITAL A∞-CATEGORIES, VOLODYMYR LYUBASHENKO, OLEKSANDR MANZYUK
- 2008

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∞-2-functor A → A∞(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∞-functor e : C → D such… (More)

- CLOSED MULTICATEGORIES, OLEKSANDR MANZYUK
- 2012

We prove that the 2-category of closed categories of Eilenberg and Kelly is equivalent to a suitable full 2-subcategory of the 2-category of closed multicategories.

We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A∞-functor categories arise as internal Hom-objects in the category of differential graded cocomplete augmented cocategories.

We prove that three definitions of unitality for A∞-categories suggested by the first author, by Kontsevich and Soibelman, and by Fukaya are equivalent.

- FREE A∞-CATEGORIES, VOLODYMYR LYUBASHENKO, OLEKSANDR MANZYUK
- 2006

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) → A1(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 generalizations of… (More)

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