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

Explores the left homotopy relation as an equivalence relation in model categories.

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

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

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Explores the basic properties of left homotopy in model categories, focusing on weak equivalences and morphism relationships.

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

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.