Galois extensions in symmetric monoidal categories

Given a ring object in a symmetric monoidal category, we can investigate what it means for an extension to be (quasi-)Galois. In this talk, I will define the degree, splitting rings and Galois closure for a separable ring object in a symmetric monoidal category, and establish a version of Galois-descent.  

Turning to modular representation theory, we can consider separable rings in the (stable) module category of a finite group over a field of prime characteristic. I will describe how restriction to a pi-point can be seen as an extension of scalars along a separable ring object. In particular, I will compute the degree and Galois closure of the ring object corresponding to the restriction to a subgroup.