GRADED LIE STRUCTURE ON COHOMOLOGY OF SOME EXACT MONOIDAL CATEGORIES

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GRADED LIE STRUCTURE ON COHOMOLOGY OF SOME EXACT MONOIDAL CATEGORIES. / Volkov, Y.; Witherspoon, S.

In: Homology, Homotopy and Applications, Vol. 26, No. 2, 2024, p. 79-98.

Research output: Contribution to journal › Article › peer-review

Author

Volkov, Y. ; Witherspoon, S. / GRADED LIE STRUCTURE ON COHOMOLOGY OF SOME EXACT MONOIDAL CATEGORIES. In: Homology, Homotopy and Applications. 2024 ; Vol. 26, No. 2. pp. 79-98.

BibTeX

@article{d8668775bc5b4333be03f53e17a70689,

title = "GRADED LIE STRUCTURE ON COHOMOLOGY OF SOME EXACT MONOIDAL CATEGORIES",

abstract = "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 {\textcopyright} 2024, International Press. Permission to copy for private use granted.",

keywords = "cohomology, exact monoidal category",

author = "Y. Volkov and S. Witherspoon",

note = "Export Date: 21 October 2024",

year = "2024",

doi = "10.4310/HHA.2024.v26.n2.a4",

language = "Английский",

volume = "26",

pages = "79--98",

journal = "Homology, Homotopy and Applications",

issn = "1532-0073",

publisher = "International Press of Boston, Inc.",

number = "2",

}

RIS

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