The Nerve and Geometric Realization

Related lectures (30)

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Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.

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

Explores counterfactuals in SEMs and D-Separation in graphical models.

Explores constructing desired adjoints in specific categories like Set.

Presents concrete examples of adjunctions between Set and Top categories.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Covers the properties of signal/data representations using Fourier transformations and matrices.

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Covers essential concepts of vectors, norms, and their properties in linear algebra.