Cellular Approximation: Homotopy and CW Complexes

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Bar Construction: Homology Groups and Classifying Space

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

The Whitehead Lemma: Homotopy Equivalence in Model Categories

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Infinity Category Theory: Lecture 2

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

Chain Homotopy and Projective Complexes

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Long Exact Sequence in Homotopy

Explores the long exact sequence in homotopy, emphasizing the importance of sets and groups in the sequence.

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.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

CW Approximation Uniqueness

Explores the uniqueness of CW approximation and Whitehead's theorem through the construction of maps inducing isomorphisms on homotopic groups.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.