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Lecture
Adjunctions and Functor Categories: Exploring Connections
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Related lectures (32)
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Free Abelian Groups: Group Theory
Explores the concept of free abelian groups as an important left adjoint functor.
Adjunctions: Constructing Desired Adjoints
Explores constructing desired adjoints in specific categories like Set.
Equivalences of Categories
Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
Limits and Colimits: Understanding Categories
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: Functors and Categories
Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.
Functors: Examples
Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.
Introduction to Category Theory: Natural Transformations
Introduces natural transformations in category theory through concrete examples from group theory.
Natural Transformations in Group Theory
Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.
Active Learning: Functors and Geometric Realization
Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.
