Homotopy Prefactorization Algebras

Author(s)
Najib Idrissi, Eugene Rabinovich.
Publication
To appear in Res. Math. Sci. (2024)
Online on
Updated on
Full text
https://cdn.idrissi.eu/main/research/homotopy-prefactorization.pdf
arXiv:2304.13011
https://arxiv.org/abs/2304.13011
hal-04082483
https://hal.science/hal-04082483

Abstract

We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space MM. This allows us to describe a notion of prefactorization algebra up to homotopy as well as morphisms up to homotopy between such objects. We make explicit these notions for several special MM, such as certain finite topological spaces, or the real line.