Functors: Definition

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Related lectures (52)

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.

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.

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: Categories and Examples Log in to Mediaspace to watch this video

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

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.

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.

Natural Transformations: Functors and Categories Log in to Mediaspace to watch this video

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

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

Explores natural transformations in algebra, defining functors and isomorphisms.

Morphism of Groups Log in to Mediaspace to watch this video

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Lie Algebra Homomorphisms Log in to Mediaspace to watch this video

Explores the association of Lie algebras to algebraic groups and homomorphisms.

Sheafification: Natural Procedure and Adjoints Log in to Mediaspace to watch this video

Covers sheafification, adjoint functors, and challenges in ensuring sheaf properties.

Free Abelian Groups and Homomorphisms Log in to Mediaspace to watch this video

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Homotopical Algebra: Theory and Applications Log in to Mediaspace to watch this video

Explores homotopical algebra, covering colimits, limits, adjunctions, and their applications in group theory.

Abelian Groups: Free Abelian Groups Log in to Mediaspace to watch this video

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Homotopical Algebra: Introduction Log in to Mediaspace to watch this video

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Active Learning: Homomorphisms and Exact Sequences Log in to Mediaspace to watch this video

Explores active learning through homomorphisms, exact sequences, and comparisons of presentations in Abelian groups.

Algebraic Structures of Morphism Spaces Log in to Mediaspace to watch this video

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Induced Homomorphisms on Relative Homology Groups Log in to Mediaspace to watch this video

Covers induced homomorphisms on relative homology groups and their properties.

RSA Encryption: Main Concepts Log in to Mediaspace to watch this video

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

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