基于范畴论推导表示论结果的参考资料请求

Hey there! Since you already have a background in finite group representation theory and you’re curious about how far we can develop representation theory from a categorical perspective—especially after learning that key results like Frobenius reciprocity can be derived using category theory—here are some top-tier references to help you explore this connection:

• Categories for the Working Mathematician (Saunders Mac Lane): The foundational text for category theory, with sections that explicitly link categorical concepts (like adjoint functors) to representation theory. It’s essential for building the theoretical bridge between the two fields.
• Representation Theory: A First Course (Fulton & Harris): A standard introductory text for representation theory that integrates categorical viewpoints at critical junctures. It includes a clear categorical treatment of Frobenius reciprocity, framing it as a consequence of adjoint induction and restriction functors.
• Categorical Representation Theory (Lecture Notes) (Peter Webb): These lecture notes are built entirely around the categorical approach to representation theory. They start with core categorical ideas (abelian categories, functors, adjoints) and use them to derive major representation theory results step-by-step.
• Group Representations and Cohomology (J. L. Alperin): This book uses category theory as a unifying framework for group representation theory, weaving categorical concepts throughout discussions of modules, induction, and more. It’s great for seeing how category theory can streamline and generalize representation arguments.

Pro tip: As you work through these, focus closely on adjoint functors and module categories—these are the categorical workhorses that underpin results like Frobenius reciprocity (which is just a specific case of the adjunction between induction and restriction functors).

内容的提问来源于stack exchange，提问作者Thomas