Lectures related to Divisibility and Torsion

Functor Hom: Abelian Groups

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

Hom Functor: Abelian Groups

Explores the Hom functor for abelian groups and its relation to direct sums.

Free Abelian Groups: Group Theory

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

Free Abelian Group: Construction and Properties

Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.

Group Theory: Free Abelian Groups

Explores free abelian groups, homomorphisms, exact sequences, and functors in group theory.

Group Actions: Equivariance and Functors

Explores equivariance in group actions and functors, demonstrating its importance in group theory.

Torsion: Hom Functoriality and Exact Sequences

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

Group Theory: Torsion and Divisibility

Covers the concepts of torsion and divisibility in group theory.

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.

Group Operations and Homomorphisms in Abelian Groups

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.

Transfer of Model Structures

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

Categories and Functors: An Introduction

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

Introduction to Category Theory: Functors

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

Adjunctions and Functor Categories: Exploring Connections

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

Invariant Definitions

Explores invariant definitions in sets, groups, and automorphisms, including p-divisible groups and free abelian groups.

Group Theory: Adjoint Functors and G-sets

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Sylow Subgroups: Group Theory

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Relation between Direct Sum and Hom

Explores the isomorphism between Hom(A, B) and Hom(A, B) for any abelian group B.

Functors and Adjunctions

Explores functors between categories and the conditions for left and right adjoints.