Forgetful functors vs. properties

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Related lectures (32)

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Functor Categories: (Co)Limits and Simplicial Sets

Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.

Group Theory: Adjoint Functors and G-sets

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Functors: Examples

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

Natural Transformations: Functors and Categories

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

Categories and Functors

Explores building categories from graphs and the encoding of information by functors.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

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.

Introduction to Category Theory: Functors

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

Introduction to Category Theory: Natural Transformations

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

Divisibility and Torsion

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.