Category Theory: Introduction

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Related lectures (37)

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.

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

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

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.

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 Log in to Mediaspace to watch this video

Covers the introduction to categories, including definitions and examples.

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.

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.

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.

Group Morphisms: G-equivariant, Chapter III Log in to Mediaspace to watch this video

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

Model Categories and Homotopy Theory: Functorial Connections Log in to Mediaspace to watch this video

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

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

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Adjunctions, Products, and Coproducts Log in to Mediaspace to watch this video

Discusses adjunctions, products, and coproducts in category theory.

Mathematics: Sets and Functions Log in to Mediaspace to watch this video

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Group Theory: Definitions and Properties Log in to Mediaspace to watch this video

Introduces group theory concepts, properties, and examples, including injective functions and group properties like associativity and inverses.

Directed Networks & Hypergraphs Log in to Mediaspace to watch this video

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Derivatives and Continuity in Multivariable Functions Log in to Mediaspace to watch this video

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

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