Left Homotopy as an Equivalence Relation: The Homotopy Relation in a Model Category

Related lectures (32)

Page 3 of 4

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

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

Explores derived functors in model categories, focusing on identity and homotopy categories.

Covers homotopies, fundamental group, and equivalence relations in applications.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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

Explores the model structure on chain complexes over a field.

Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.