Abstract Let

Let R be a commutative noetherian ring and let $$\mathfrak {a}$$ an ideal of R. In this paper, we study certain condition, namely $$C_{\mathfrak {a}}$$ , introduced by Aghapournahr Melkersson, on the extension two subcategories R-modules. We develop some main results Yoshizawa (Proc Am Math Soc 140(7):2293–2305, 2012; J Commut Algebra 13:137–155, 2021). As example subcategories, weakly Laskeria...

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes characterization subcategories which are closed under action, and classification factor as product pointed transitive in terms pseudoinvertible objects. As an application, we classify two orbits simple objects nontrivial grading group.