Lectures related to Categorical Perspective: Group Actions

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.

Functors: Definition

Introduces functors in category theory and explains their composition.

The Regular Representation

Introduces the regular representation, a key tool for studying group actions on varieties.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Endomorphisms: Matrix Equivalence

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Group Theory: Recalls

Offers a recap on group theory, focusing on linear applications and bases.

Linear Representations: Basics and Examples

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Restriction Functors: Group Actions

Introduces the concept of restriction functors in group actions.