Lectures related to Restriction Functors: Group Actions

Functors: Definition

Introduces functors in category theory and explains their composition.

Group Theory: Restriction Functor

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

Natural Transformations: Examples and Applications

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

Categories and Functors: An Introduction

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Natural Transformations

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

Group Cohomology

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

Adjunctions and Functor Categories: Exploring Connections

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

Limits and colimits: Introduction, Chapter 1(c)

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

Free Abelian Groups: Group Theory

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

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

Limits and Colimits in Functor Categories

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

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.

Transfer of Model Structures

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

Category Theory: G-sets and Left Adjoint Functor

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

Active Learning in Category Theory

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Simplicial and Cosimplicial Objects: Examples and Applications

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

Limits and colimits as adjoints: Chapter 1(c)

Explores the characterization of limits and colimits as adjoints in category theory.