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Why Quasicategories?
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Related lectures (32)
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Quillen pairs and Quillen equivalences: Derived functors
Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.
Quillen Equivalences
Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.
Homotopy Theory of Chain Complexes
Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
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.
Quasi-Categories: Active Learning Session
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Homotopy Categories: Model Structures
Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.
Derived functors: Two technical lemmas
Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.
