Lecture

Functors and Homomorphisms in Group Theory

Related lectures (32)

Covers special cases in group theory, focusing on group actions and functors.

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

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Covers the adjoints of the restriction functor in group theory.

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

Explores the Hom functor for abelian groups and its relation to direct sums.

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

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Introduces subgroups and homomorphisms in group theory, with examples for illustration.

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

Introduces functors in category theory and explains their composition.

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

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

Introduces the concept of restriction functors in group actions.

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.

Provides an overview of categories, functors, and natural transformations in mathematics.

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.