Lectures related to Fixed Points and Orbits Analysis: Group Actions

Simplicial and Cosimplicial Objects: Examples and Applications

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

Active Learning Session: Group Theory

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

Free Abelian Groups: Group Theory

Explores the concept of free abelian groups as an important left adjoint functor.

Introduction to Category Theory: Natural Transformations

Introduces natural transformations in category theory through concrete examples from group theory.

Natural Transformations in Group Theory

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Introduction to Category Theory: Adjoint Functors

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

Active Learning Session

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

Triangular Identities

Covers triangular identities, natural transformations, commutative diagrams, and adjunction notation in group and category theory.

Basic Notions, Ch III: Group Actions

Explores group actions on sets, orbits, fixed points, and classic results.

Group Actions and Functors

Covers group quotient, group actions, and functors connecting sets and G-sets.

Category Theory: G-sets and Left Adjoint Functor

Explores the construction of G-sets and left adjoint functors in category theory.

Group Theory: Restriction Functor

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

Direct Sums: Lemme 1.2

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Generalization of Category Equivalence

Introduces an important generalization of category equivalence and its implications for group theory.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Important Facts of Fixed Points and Orbits

Explores group actions, fixed points, orbits, Equation of Class, and Burnside's Lemma.

Class Equation and Burnside's Lemma

Explores the class equation and Burnside's lemma in group theory.

Exam Information

Covers details of the upcoming theoretical exam, including structure and guidelines.

Equivalences of Categories

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Limits and Colimits: Understanding Categories

Explores limits and colimits in category theory, discussing their definitions, properties, and applications, including the non-existence of limits in certain categories and the relationships between limits and colimits under functors.