Category Theory For Beginners: Abstract Algebra
Using a category theory perspective we define groups, group homomorphisms, Lie groups, quotient groups, group actions, rings, modules, vector spaces and fields. We also examine several features of the category of groups and discuss related adjunctions and monads. In particular we look at free groups, Cayley's Theorem, the orbit-stabilizer theorem, the orbit category, normal subgroups. We also define Abelian groups and their tensor products.
Some of this material is inspired by Richard Blocherds' group theory YouTube playlist
• Group theory 1: Introduction
We also use material from Riehl's book
https://math.jhu.edu/~eriehl/context.pdf