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Related lectures (50)

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.

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.

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.

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

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Model Categories: Properties and Structures Log in to Mediaspace to watch this video

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

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.

Homotopy Categories: Model Structures Log in to Mediaspace to watch this video

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

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.

Monstrous Moonshine Log in to Mediaspace to watch this video

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

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.

Morphism of Groups Log in to Mediaspace to watch this video

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

Groups: Definitions, Properties, and Homomorphisms Log in to Mediaspace to watch this video

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Eshelby Method: Modulus Mismatch and Eigenstrains Log in to Mediaspace to watch this video

Discusses stress concentrations, modulus mismatch, and eigenstrains in materials.

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.

Shor's algorithm: quantum circuit Log in to Mediaspace to watch this video

Covers the implementation of Shor's algorithm on a quantum circuit, including the analysis of quantum Fourier transform.

Approximation by Smooth Functions Log in to Mediaspace to watch this video

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Group Theory: Direct Sum of Abelian Groups Log in to Mediaspace to watch this video

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Quantum Eigenfunctions Log in to Mediaspace to watch this video

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Coxeter Groups: Generators and Relations Log in to Mediaspace to watch this video

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

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