Abstract
 In this talk, I will consider separable (commutative) monoids in a tensor
triangulated category and show how they pop up in various settings.
In modular representation theory, for instance, restriction to a
subgroup can be thought of as extension along a separable monoid in
the (stable or derived) module category. In algebraic geometry,
separable monoids correspond to \'{e}tale extensions of schemes. But
separable monoids are nice for various reasons, beyond the analogy with
\'{e}tale topology; they allow for a notion of degree, have splitting ring
extensions, and one can define (quasi)Galois extensions.
