Euler Characteristic: Surfaces and Homotopy

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Elementary Properties of Model Categories

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

Cell Attachment and Homotopy

Covers cell attachment, homotopy, mappings, and universal properties in topology.

Homotopy Invariance

Explores homotopy invariance, emphasizing the preservation of properties under continuous functions and their relationship with topological spaces.

Universal Covering Construction

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

Unifying left and right homotopy: The homotopy relation

Explores the equivalence of left and right homotopy for morphisms between bifibrant objects.

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.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Homotopy Classes and Group Structures

Explores wedges in pointed spaces, group structures, and the Echman-Hilton argument.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Base B for the covering

Explores constructing a base B for a topology using homotopy classes and paths.