I’ve been participating in the Kan Extension Seminar II, and this week it’s my turn to post about Jon Beck’s “Distributive Laws” at the n-Category Cafe!

The post uses lots of string diagrams for monads, resulting in pictures like the following:

See you there!

In this post, I’ll demonstrate 3 ways to define non-commutative rings in Sage. They’re essentially different ways of expressing the non-commutative relations in the ring:

1. Via g_algebra: define the relations directly
2. Via NCPolynomialRing_plural: define a pair of structural matrices
3. Via a quotient of a letterplace ring: define the ideal generated by the relations (only works for homogeneous relations)

This post illustrates some of SageMath’s character theory functionality, as well as some basic results about characters of finite groups.