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Related lectures (32)

Page 3 of 4

Quasicategories: An Alternative Homotopy Theory

Introduces quasicategories as an alternative approach to defining homotopy maps and categories.

Homotopy Category and Derived Functors

Explores the homotopy category of chain complexes and the relation between quasi-isomorphisms and chain homotopy equivalences.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Lifting properties and model categories

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

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.

Natural Transformations

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

Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.

From Simplicial Categories to Quasicategories

Introduces the construction of quasi-categories from Kan enriched categories through defining simplicially enriched categories and constructing the simplicial nerve functor.

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.

Infinity Category Theory: Extensions and Equivalences

Explores right extensions in infinity category theory and their equivalent definitions.