There’s a two-post series on “tensor products for group actions”:
Tensor Products for Group Actions, Part 1
Tensor Products for Group Actions, Part 2
There’s an ongoing series on representation theory:
A First Impression of Group Representations
The Group Algebra: Another Perspective on Representations
Semisimplicity and Representations, Part 1
Semisimplicity and Representations, Part 2
An Introduction to Character Theory
With an “appendix” on category theory that can also be read independently:
A Brief Introduction to Categories, Part 1: Categories
A Brief Introduction to Categories, Part 2: Functors
A Brief Introduction to Categories, Part 3: Natural Transformations and Equivalences
A Brief Introduction to Categories, Part 4: The Yoneda Lemma
A Brief Introduction to Categories, Part 5: Universal Properties and Representable Functors
A Brief Introduction to Categories, Part 6: Some Examples of Limits and Colimits
A Brief Introduction to Categories, Part 7: General Limits and Colimits
Without Loss of Universality 