Blog

Say $ X$ is a smooth projective variety over $ \mathbf{C}$ , and $ \mathcal{X} = X^{\rm an}$ its $ \mathbf{C}$ -analytic space. For what integers $ i,d$ is the Deligne cohomology $ H^i_{\mathcal{D}}(\mathcal{X},\mathbf{Z}(d))$ of $ \mathcal{X}$ , finitely generated/a compact group in some (any, I don’t know) suitable sense?Read more

I read the following statement (equation 22) in “Monoidal 2-structure of bimodule categories” by Justin Greenough: Let $ \mathcal{C}$ be a finite tensor category (abelian k-linear rigid monoidal category with simple unit and finite dimensional Hom spaces). Let $ \mathcal{M}$ and $ \mathcal{N}$ be exact left module categories over $ \mathcal{C}$ . We introduce theRead more

Let $ \mathcal{C}$ be a fusion category, and $ \mathcal{M}, \mathcal{N}$ semisimple $ (\mathcal{C}, \mathcal{C})$ -bimodule categories. The left $ \mathcal{C}$ -action is denoted as $ – \triangleright – \colon \mathcal{C} \boxtimes \mathcal{M} \to \mathcal{M}$ , analogously the right action. A relative half-braiding on an object $ M \in \operatorname{ob} \mathcal{M}$ is an natural isomorphismRead more