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Related lectures (32)
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Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Serre model structure: Left and right homotopy
Explores the Serre model structure, focusing on left and right homotopy equivalences.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
Derived Functors in Homotopical Algebra
Covers the Fundamental Theorem of homotopical algebra, Quillen pairs, and derived functors.
The Topological Künneth Theorem
Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.
Homotopy Category of a Model Category
Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.
Derived functors: Two technical lemmas
Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.
Adjunction between Simplicial Sets and Enriched Categories
Covers the adjunction between simplicial sets and simplicially enriched categories, including preservation of inclusions and construction of homotopy categories.
