Introduction to Category Theory: Categories and Examples

Related lectures (32)

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

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

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

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

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

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

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

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

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

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

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

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

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