Lectures related to Derived functors: Two technical lemmas

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

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

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

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

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

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

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 model structure on chain complexes over a field.

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

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

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

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

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

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

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

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

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

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

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