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of 30
pro vyhledávání: '"Manzyuk, Oleksandr"'
Autor:
Manzyuk, Oleksandr, Pearlmutter, Barak A., Radul, Alexey Andreyevich, Rush, David R., Siskind, Jeffrey Mark
Forward Automatic Differentiation (AD) is a technique for augmenting programs to compute derivatives. The essence of Forward AD is to attach perturbations to each number, and propagate these through the computation. When derivatives are nested, the d
Externí odkaz:
http://arxiv.org/abs/1211.4892
Autor:
Manzyuk, Oleksandr
Differential lambda-categories were introduced by Bucciarelli et al. as models for the simply typed version of the differential lambda-calculus of Ehrhard and Regnier. A differential lambda-category is a cartesian closed differential category of Blut
Externí odkaz:
http://arxiv.org/abs/1202.0411
Autor:
Manzyuk, Oleksandr
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.
Comment: 34 pages
Comment: 34 pages
Externí odkaz:
http://arxiv.org/abs/0904.3137
Publikováno v:
Problems of topology and related questions, Proc. of Inst. of Mathematics, NASU, Kyiv, 3 (2006) No. 3, 235-268
We prove that three definitions of unitality for A-infinity-categories suggested by the first author, by Kontsevich and Soibelman, and by Fukaya are equivalent.
Comment: 19 pages, LaTeX, close to published version
Comment: 19 pages, LaTeX, close to published version
Externí odkaz:
http://arxiv.org/abs/0802.2885
Publikováno v:
Geometry and Dynamics of Groups and Spaces, Progress in Math., 265, Birkhauser, Basel (2007) 565-645
We define A-infinity-bimodules similarly to Tradler and show that this notion is equivalent to an A-infinity-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground commutative
Externí odkaz:
http://arxiv.org/abs/math/0701165
Autor:
Keller, Bernhard, Manzyuk, Oleksandr
Publikováno v:
Journal of Homotopy and Related Structures, vol. 2 (2007), no. 1, pp. 85-97
We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A-infinity functor categories arise as internal Hom-objects in the category of differential graded cocomplete aug
Externí odkaz:
http://arxiv.org/abs/math/0612175
Publikováno v:
Theory and Applications of Categories, 16 (2006) No. 9, 174-205
For a differential graded k-quiver Q we define the free A-infinity-category FQ generated by Q. The main result is that for an arbitrary A-infinity-category A the restriction A-infinity-functor A_\infty(FQ,A) -> A_1(Q,A) is an equivalence, where objec
Externí odkaz:
http://arxiv.org/abs/math/0312339
For a full subcategory B of a unital A_infinity-category C a quotient unital A_infinity-category `C/B' is defined. For differential graded categories such quotient is constructed by V.Drinfeld. Our construction is explicit and uses freely generated A
Externí odkaz:
http://arxiv.org/abs/math/0306018
Autor:
Manzyuk, Oleksandr.
Publikováno v:
kostenfrei.
Kaiserslautern, Techn. University, Diss., 2007.
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