Abelian Groups: Category Theory

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Related lectures (51)

Characters and Dirichlet's Theorem Log in to Mediaspace to watch this video

Introduces characters over a finite abelian group and explains the proof of the infinitude of primes in arithmetic progressions.

Galois Theory: Solvability and Radical Extensions Log in to Mediaspace to watch this video

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Abelian p-groups: Groupes abéliens Log in to Mediaspace to watch this video

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Direct Sums Arithmetic Log in to Mediaspace to watch this video

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Sylow Subgroups: Group Theory Log in to Mediaspace to watch this video

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Kirillov Paradigm for Heisenberg Group Log in to Mediaspace to watch this video

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

The Torus and Linear Groups Log in to Mediaspace to watch this video

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Diffeomorphism and implicit functions Log in to Mediaspace to watch this video

Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.

Microwave Circuit Characterization: Flow Charts and Reduction Rules Log in to Mediaspace to watch this video

Covers circuit characterization using flow charts and reduction rules.

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