Introduction to Left Homotopy: The Homotopy Relation in a Model Category

Related lectures (32)

Page 2 of 4

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

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

Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.

Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.

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

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

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

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.