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Lecture
Homotopy Category and Derived Functors
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Related lectures (32)
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Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.
Chain Homotopy and Projective Complexes
Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Quillen Equivalences
Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.
Homotopy Theory: Cylinders and Path Objects
Covers cylinders, path objects, and homotopy in model categories.
Understanding Lifting Properties in Homotopy Theory
Focuses on lifting properties in homotopy theory of chain complexes.
Construction of the homotopy category
Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.
Homotopical Algebra: The Homotopy Category of a Model Category
Focuses on proving the construction of the homotopy category and its properties, including preservation of composition and uniqueness of functors.
Group Actions: Quotients and Homomorphisms
Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.
Derived Functors in Homotopical Algebra
Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.
