Graded Lie structure on cohomology of some exact monoidal categories
Y Volkov, S Witherspoon�- arXiv preprint arXiv:2004.06225, 2020 - arxiv.org
Y Volkov, S Witherspoon
arXiv preprint arXiv:2004.06225, 2020•arxiv.orgFor 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 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�…
topological and algebraic definitions of the Lie bracket on the extension algebra of the unit
object. The topological definition, due to Schwede and 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�…
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 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 -coderivation and homotopy lifting techniques from bimodule categories to these exact monoidal categories.
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