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Lecture
Quillen Equivalences
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Related lectures (32)
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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.
Homotopy Category and Derived Functors
Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.
Lifting properties and model categories
Covers the study of lifting properties in categories, focusing on the left and right lifting properties.
Homotopy Theory of Chain Complexes
Explores the model structure on chain complexes over a field.
Construction of the homotopy category
Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.
Introduction to Model Categories
Explores lifting properties and model categories in topological spaces.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Homotopy Theory in Care Complexes
Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.
Existence of Left Derived Functors: Part 2
Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.
