Retracte: Fundamental Group and Cell Attachment

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Page 3 of 4

Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.

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

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

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

Explores path lifting, homotopy properties, and homomorphisms in covering spaces.

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

Covers commutative diagrams, homotopy, and constructing topological spaces.

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

Introduces the homotopy extension property, exploring conditions for extending continuous maps.