Lectures related to Introduction to Category Theory: Categories and Examples

Concrete Categories

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

Introduction to Category Theory: Examples

Introduces the theory of categories through examples and discusses the product of categories.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Functors: Definition

Introduces functors in category theory and explains their composition.

Category Theory: Introduction

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

Group Theory: Restriction Functor

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

Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

Free Abelian Groups and Homomorphisms

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Active Learning Session: Group Theory

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

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Representation Theory: Algebras and Homomorphisms

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

Group Morphisms: G-equivariant, Chapter III

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

Natural Learning Session

Explores coproducts, universal properties, and natural transformations in category theory.

Functor Hom: Abelian Groups

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Direct Sums of Abelian Groups

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Free Abelian Groups: Group Theory

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