Lectures related to The Whitehead Lemma: Homotopy Equivalence 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.

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

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

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

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

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

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

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

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

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

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.

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

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

Introduces left homotopy between morphisms and its preservation under postcomposition in a model category.

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.