Natural Transformations and Functors

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Related lectures (36)

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.

Natural Learning Session Log in to Mediaspace to watch this video

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

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

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

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.

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

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

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.

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.

Introduction to Category Theory: Adjunctions (Part 1)Log in to Mediaspace to watch this video

Explores the definition of adjunctions and the relationship between functors.

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

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

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.

Equivalences de Catégories et Adjonctions Log in to Mediaspace to watch this video

Explores category equivalences, adjunctions, and group actions in category theory.

Free Actions, Ch III: Group Actions Log in to Mediaspace to watch this video

Explains the concept of free actions and their preservation properties in group theory.

Cohomology: Recollection and Foliations Log in to Mediaspace to watch this video

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Naturality: Chain Complexes and Homology Groups Log in to Mediaspace to watch this video

Explores naturality in chain complexes, homology groups, and abelian groups, emphasizing the commutativity of squares and the Five-Lemma.

Long Exact Sequence of Ext-Modules Log in to Mediaspace to watch this video

Covers the construction of long exact sequences of Ext-modules and provides illustrative examples.

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