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

A Brief Introduction to Categories, Part 8: Adjunctions I

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