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Related lectures (32)

Decomposing CW complexes

Covers the decomposition of a CW complex based on characteristic maps and cell containment.

The Joyal Model Structure

Defines and studies the Joyal Model structure, focusing on the properties of quasi-categories within this framework.

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.

Limits and colimits as adjoints: Chapter 1(c)

Explores the characterization of limits and colimits as adjoints in category theory.

Bar Construction: Homology Groups and Classifying Space

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

Cellular Approximation: Homotopy and CW Complexes

Explores the cellular approximation theorem for CW complexes and its implications on homotopy groups.

Homotopic Extension Problem

Explores solving the homotopic extension problem, constructing relative CW complexes, and ensuring uniqueness in CW approximations.

Simplicial Homology: Examples

Explores examples of simplicial homology by equipping known topological spaces with delta complex structures.

Simplices

Covers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.

Singular homology

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

Homology and the fundamental group

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

Review of Simplicial Sets

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

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