Concept
Localization of a category
Related lectures (21)
Introduction to Model Categories
Explores lifting properties and model categories in topological spaces.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
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.
Steenrod Squares
Covers the concept of Steenrod Squares and their applications in stable cohomology operations.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Model Category: Definition and Elementary Properties
Covers the definition and properties of a model category, including fibrations, cofibrations, weak equivalences, and more.
Homotopy Category of a Model Category
Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.
Existence of Left Derived Functors
Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.
Introduction to Derived Functors: Left and Right Derived Functors
Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.