Fundamental groupoid

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Discusses fundamental groups, surfaces, and their topological properties in detail.

Covers student feedback, group exercises, and fundamental topology concepts, emphasizing the importance of understanding coverings and group actions.

Delves into cell attachment, exploring its implications for different cell dimensions.

Explores the lifting criterion for maps between path-connected and locally path-connected spaces.

Covers the construction of a telescope using cylinders on circles and the calculation of fundamental groups for various spaces.

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

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

Explores the concept of category theory, providing examples and discussing the opposite category concept.

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.