BIMSA > Disquisitions on Monoidal Categories and Operads Disquisitions on Monoidal Categories and Operads Deformation Theory of $\mathbb{E}_n$-Monoidal Categories
Deformation Theory of $\mathbb{E}_n$-Monoidal Categories
Organizers
Svyatoslav Pimenov , Angel Toledo Castro
Speaker
Yining Chen
Time
Monday, April 20, 2026 4:00 PM - 5:00 PM
Venue
A3-1-301
Online
Zoom 559 700 6085 (BIMSA)
Abstract
Fix a field $k$ of characteristic $0$. It is well known that the deformation theory of a (plain) $k$-linear category $\mathcal{C}$ is controlled by its Hochschild cohomology i.e. $\mathrm{End}_{\mathrm{End}(\mathcal{C})}(1)$, which is an $\mathbb{E}_2$-algebra. In this talk, I will describe which (non-unital) $\mathbb{E}_{n+2}$-algebra controls the deformation theory of $\mathbb{E}_n$-monoidal categories and its applications to deformation quantization with respect to shifted Poisson structures. Then I will consider the example of $\mathbf{Rep}(G)$. If time permits, I will also talk about the relation of factorization homology and deformations. An example of it is that as proved by Ben-Zvi-Brochier-Jordan, the factorization homology of $\mathbf{Rep}_{\hbar}(G)$ gives a formal deformation of the category of sheaves on the character variety.