Quasicategories: An Alternative Homotopy Theory

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Page 3 of 4

Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.

Homotopy Categories: Model Structures

Explores homotopy categories in model structures, emphasizing weak equivalences and the Whitehead Lemma.

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.

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Homotopy Category of a Model Category

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

Why Quasicategories?

Discusses the benefits of quasi-category theory and model structures.

Quillen pairs and Quillen equivalences: Derived functors

Explores Quillen pairs, equivalences, and derived functors in homotopical algebra.

Natural Transformations

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.