Categorical Perspective: Group Actions

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Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Group Morphisms: G-equivariant, Chapter III

Discusses the formulation of G-morphisms within vector spaces and topological spaces.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Introduction to Category Theory: Categories and Examples

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

Group Theory: Restriction Functor

Explores the restriction functor in group theory, focusing on its properties.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Introduction to Category Theory: Adjoint Functors

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.