Lectures related to Existence of Left Derived Functors: Part 2

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

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

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

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

Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.

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

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

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

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

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

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

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

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

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

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

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

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.