Active Learning: Group Theory

Related lectures (38)

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Explores the construction of G-sets and left adjoint functors in category theory.

Explores group actions, defining functors on groups, and verifying properties of group actions.

Explores examples of categories, morphisms, groupoids, and functors in category theory.

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

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

Explores category equivalences, adjunctions, and group actions in category theory.

Explores the concept of free abelian groups as an important left adjoint functor.

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

Introduces the basics of group theory, defining groups, categories, and groupoids.

Explores group actions on spaces, including fixed points and non-trivial actions.

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

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

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

Explores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.

Explores rings, domains, fields, and ideals, with a focus on constructions and properties.

Covers the theory and assumptions behind transmission lines, including TEM mode of propagation and antenna mode currents.

Page 2 of 2