Geodesic
Graded Lie structure on cohomology of some exact monoidal categories
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 79-98.

Voir la notice de l'article provenant de la source International Press of Boston

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 $A_\infty$-coderivation and homotopy lifting techniques from bimodule categories to these exact monoidal categories.
DOI : 10.4310/HHA.2024.v26.n2.a4
Classification : 16E40, 18G15 
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Y. Volkov; S. Witherspoon. Graded Lie structure on cohomology of some exact monoidal categories. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 79-98. doi : 10.4310/HHA.2024.v26.n2.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a4/

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