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GRADED LIE STRUCTURE ON COHOMOLOGY OF SOME EXACT MONOIDAL CATEGORIES. / Volkov, Y.; Witherspoon, S.
в: Homology, Homotopy and Applications, Том 26, № 2, 2024, стр. 79-98.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - GRADED LIE STRUCTURE ON COHOMOLOGY OF SOME EXACT MONOIDAL CATEGORIES
AU - Volkov, Y.
AU - Witherspoon, S.
N1 - Export Date: 21 October 2024
PY - 2024
Y1 - 2024
N2 - For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on the extension algebra of the unit object. The topological definition, due to Schwede and to Hermann, involves loops in extension categories. The algebraic definition, due to the first author, involves homotopy liftings of maps. As a consequence of our description, we prove that the topological definition indeed yields a Gerstenhaber algebra structure in this monoidal category setting. This answers a question of Hermann for those exact monoidal categories in which the unit object has a particular type of resolution that is called power flat. For use in proofs, we generalize A∞-coderivation and homotopy lifting techniques from bimodule categories to these exact monoidal categories. Copyright © 2024, International Press. Permission to copy for private use granted.
AB - For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on the extension algebra of the unit object. The topological definition, due to Schwede and to Hermann, involves loops in extension categories. The algebraic definition, due to the first author, involves homotopy liftings of maps. As a consequence of our description, we prove that the topological definition indeed yields a Gerstenhaber algebra structure in this monoidal category setting. This answers a question of Hermann for those exact monoidal categories in which the unit object has a particular type of resolution that is called power flat. For use in proofs, we generalize A∞-coderivation and homotopy lifting techniques from bimodule categories to these exact monoidal categories. Copyright © 2024, International Press. Permission to copy for private use granted.
KW - cohomology
KW - exact monoidal category
UR - https://www.mendeley.com/catalogue/46df9e1a-73dc-3e2d-b55b-4bb04eff54de/
U2 - 10.4310/HHA.2024.v26.n2.a4
DO - 10.4310/HHA.2024.v26.n2.a4
M3 - статья
VL - 26
SP - 79
EP - 98
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
SN - 1532-0073
IS - 2
ER -
ID: 126221040