Introduction to Category Theory: Categories and Examples

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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.