Equivalences of Categories

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Related lectures (52)

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.

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.

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

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

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

Explores the concept of category theory, providing examples and discussing the opposite category concept.

Active Learning Session Log in to Mediaspace to watch this video

Explores the verification of a Lie functor as a left adjoint, with natural transformations satisfying triangular identities and isomorphisms.

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.

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.

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

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

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.

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

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

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.

Category Theory: Natural Transformations and Adjunctions Log in to Mediaspace to watch this video

Explores natural transformations and adjunctions in category theory, illustrating concepts through concrete examples and discussing the conditions for the existence of adjoints.

An Introduction to Category Theory: Products and Coproducts Log in to Mediaspace to watch this video

Demonstrates how adjoints preserve coproducts and products in category theory.

Functors and Homomorphisms in Group Theory Log in to Mediaspace to watch this video

Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.

Orbital and Fixed Point Functors Log in to Mediaspace to watch this video

Formalizes the construction of orbits and fixed points in group actions, defining morphisms and verifying naturalness.

Exam Information Log in to Mediaspace to watch this video

Covers details of the upcoming theoretical exam, including structure and guidelines.

Derived functors: Identity and Homotopy Categories Log in to Mediaspace to watch this video

Explores derived functors in model categories, focusing on identity and homotopy categories.

Quotient Groups: Homomorphisms and Isomorphisms Log in to Mediaspace to watch this video

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Homotopical Algebra: Examples and Adjunctions Log in to Mediaspace to watch this video

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

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