Nerves and Geometric Realization

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Related lectures (32)

Page 2 of 4

Quasi-Categories: Active Learning Session

Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.

Geometric Realization in Model Categories

Explores geometric realization, simplicial sets, and model category structures.

Singular homology

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

Natural Examples of Simplicial Sets

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

Simplicial Homology Revisited

Covers the concept of simplicial homology, focusing on finite complexes and induced maps.

Homotopy Invariance: Homology Groups

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

Homology Groups: Basics

Introduces reduced homology groups and explains their properties and applications in topology.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Acyclic Models: Cup Product and Cohomology

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.