Homotopy Equivalence in Chain Complexes

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Homotopy theory of chain complexes

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.

Homotopy Theory of Chain Complexes

Explores the model structure on chain complexes over a field.

Elementary Properties of Model Categories

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

Cell Attachment and Homotopy

Explores cell attachment, homotopy, function existence, construction using universal property, and continuity.

Cylinder Construction on Chain Complex

Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.

Base B for the covering

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

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.

Infinity Category Theory: Lecture 2

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