Homotopical Algebra Exam

Related lectures (23)

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

Explores natural transformations in algebra, defining functors and isomorphisms.

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

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

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

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

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

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

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

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