Fundamental groupoid

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Higher Homotopy Groups: Generalization and Structure

Explores the generalization and structure of higher homotopy groups, including their abelianness, historical context, and properties of H spaces.

Categories: Functors, and Natural Transformations

Introduces categories, concrete examples, opposite categories, and isomorphisms, leading to groupoids.

Retracte: Fundamental Group and Cell Attachment

Covers the concept of a subspace being a retract of another space and fundamental groups, including examples like contracting the teeth of a necklace.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Topology: Homotopy and Cone Attachments

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

The Degree of a Covering Space

Shows the equivalence between the index of a covering space's fundamental group and the degree of the covering space.

Universal Covering

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

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.

Homology: Introduction and Applications

Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.

Linear Applications: Change of Basis

Explores changing the base of linear applications and calculating vector images in different bases, emphasizing the use of canonical basis.