Category theory

Related lectures (32)

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Functors: Examples

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

Category Theory: Introduction Log in to Mediaspace to watch this video

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Natural Transformations in Algebra Log in to Mediaspace to watch this video

Explores natural transformations in algebra, defining functors and isomorphisms.

Natural Transformations Log in to Mediaspace to watch this video

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

Category Theory: Introduction Log in to Mediaspace to watch this video

Explores the concept of category theory, providing examples and discussing the opposite category concept.

Active Learning in Category Theory Log in to Mediaspace to watch this video

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

Natural Transformations: Examples and Applications Log in to Mediaspace to watch this video

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

Natural Transformations: Functors and Categories Log in to Mediaspace to watch this video

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

Invariant Definitions Log in to Mediaspace to watch this video

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

Limits and Colimits: Understanding Categories Log in to Mediaspace to watch this video

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.

Introduction to Category Theory: Natural Transformations Log in to Mediaspace to watch this video

Covers the concept of natural transformations between functors and their associativity.