Lectures related to Construction of Free Action Functor

Categories and Functors: An Introduction

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

Free Abelian Groups: Group Theory

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

Category Theory: G-sets and Left Adjoint Functor

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

Simplicial and Cosimplicial Objects: Examples and Applications

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

Group Actions and Functors

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

Active Learning Session

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Introduction to Category Theory: Natural Transformations

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

Introduction to Category Theory: Functors

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Natural Transformations in Group Theory

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

Limits and colimits: Introduction, Chapter 1(c)

Introduces limits and colimits in a category, covering their properties and uniqueness.

Adjunctions and Functor Categories: Exploring Connections

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Functors: Examples

Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Group Theory: Subgroups and General Group Actions

Explores group actions, defining functors on groups, and verifying properties of group actions.

Natural Transformations: Examples and Applications

Explores natural transformations between functors in different categories and their applications.

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.

Active Learning Session

Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.