Geodesic
Homotopy characters as a homotopy limit
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 1-20.

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

For a Hopf DG‑algebra corresponding to a derived algebraic group, we compute the homotopy limit of the associated cosimplicial system of DG‑algebras given by the classifying space construction. The homotopy limit is taken in the model category of DG‑categories. The objects of the resulting DG‑category are Maurer–Cartan elements of $\operatorname{Cobar}(A)$, or 1‑dimensional $A_\infty$-comodules over $A$. These can be viewed as characters up to homotopy of the corresponding derived group. Their tensor product is interpreted in terms of Kadeishvili’s multibraces. We also study the coderived category of DG‑modules over this DG‑category.
DOI : 10.4310/HHA.2024.v26.n2.a1
Classification : 18A30, 55U35
Keywords: homotopy limit, representation up to homotopy, homotopy character, homotopy monoidal structure 
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Sergey Arkhipov; Daria Poliakova. Homotopy characters as a homotopy limit. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 1-20. doi : 10.4310/HHA.2024.v26.n2.a1. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a1/

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