Introduction to Category Theory: Natural Transformations

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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.

Active Learning Session Log in to Mediaspace to watch this video

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

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 Learning Session Log in to Mediaspace to watch this video

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

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

Introduces natural transformations in category theory through concrete examples from group theory.

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 in Algebra Log in to Mediaspace to watch this video

Explores natural transformations in algebra, defining functors and isomorphisms.

Category Theory: G-sets and Left Adjoint Functor Log in to Mediaspace to watch this video

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

Free Abelian Groups: Group Theory Log in to Mediaspace to watch this video

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

Group Actions and Functors Log in to Mediaspace to watch this video

Covers group quotient, group actions, and functors connecting sets and G-sets.

Equivalences of Categories Log in to Mediaspace to watch this video

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Group Theory: Subgroups and General Group Actions Log in to Mediaspace to watch this video

Explores group actions, defining functors on groups, and verifying properties of group actions.

Active Learning: Group Theory Log in to Mediaspace to watch this video

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

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