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Related lectures (32)

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Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Extensions to Exchangeability: Statistical Analysis of Network Data

Covers extensions to exchangeability in network data analysis, including graphon frameworks and edge exchangeability.

Simplicial Sets: Introduction and Products

Introduces simplicial sets and explores the construction of products with a geometric interpretation.

Schematic Models: Quasi-Categories and ∞-Groupoids

Covers schematic models, emphasizing quasi-categories and ∞-groupoids in modeling categories.

Homotopy Invariance: Homology Groups

Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.

Infinity Category Theory: Lecture 2

Explores infinity category theory, covering ABB, Kao-cosmos, homotopy, categories, and equivalences.

Review of Simplicial Sets

Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Singular homology

Introduces singular homology, defining singular simplices and explaining the chain complex construction.

From Simplicial Categories to Quasicategories

Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.