Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Lyubashenko, Volodymyr"'
Autor:
Lyubashenko, Volodymyr
We construct a machine which takes as input a locally small symmetric closed complete multicategory $\mathsf V$. And its output is again a locally small symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the multicategory of smal
Externí odkaz:
http://arxiv.org/abs/2304.11227
Autor:
Lyubashenko, Volodymyr
We recall the notions of a graded cocategory, conilpotent cocategory, morphisms of such (cofunctors), coderivations and define their analogs in $\mathbb L$-filtered setting. The difference with the existing approaches: we do not impose any restrictio
Externí odkaz:
http://arxiv.org/abs/2010.05242
Autor:
Lyubashenko, Volodymyr
We provide bar and cobar constructions as functors acting between various categories of curved operads and curved cooperads. Cobar and bar constructions are adjoint to each other. Given a twisting cochain between a curved augmented cooperad C with an
Externí odkaz:
http://arxiv.org/abs/1403.3644
Autor:
Lyubashenko, Volodymyr
We describe the category of homotopy coalgebras, concentrating on properties of relatively cofree homotopy coalgebras, morphisms and coderivations from an ordinary coalgebra to a relatively cofree homotopy coalgebra, morphisms and coderivations betwe
Externí odkaz:
http://arxiv.org/abs/1402.0408
Autor:
Lyubashenko, Volodymyr
Publikováno v:
Matematychni Studii, V.40 (2013) No.2 , 115-131
We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other.
Comment: 23 pages, to appear in Matematychni
Comment: 23 pages, to appear in Matematychni
Externí odkaz:
http://arxiv.org/abs/1311.7681
Autor:
Lyubashenko, Volodymyr
We prove a theorem of Hinich type on existence of a model structure on a category related by an adjunction to the category of differential graded modules over a graded commutative ring.
Comment: 15 pages, the article is simplified: instead of tw
Comment: 15 pages, the article is simplified: instead of tw
Externí odkaz:
http://arxiv.org/abs/1205.6066
Autor:
Lyubashenko, Volodymyr
Publikováno v:
J. Algebra 329 (2011), no. 1, 190-212
It is well known that the differential graded operad of A_infinity-algebras is a cofibrant replacement (a dg-resolution) of the operad of associative differential graded algebras without units. In this article we find a cofibrant replacement of the o
Externí odkaz:
http://arxiv.org/abs/1205.6058
Autor:
Lyubashenko, Volodymyr
Publikováno v:
Theory and Applications of Categories, Vol. 30, 2015; No. 45, pp 1501-1551; No. 46, pp 1552-1623
We show that morphisms from n A_infinity-algebras to a single one are maps over an operad module with n+1 commuting actions of the operad A_infinity, whose algebras are conventional A_infinity-algebras. Similar statement holds for homotopy unital A_i
Externí odkaz:
http://arxiv.org/abs/1205.6072
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