Quillen pairs and Quillen equivalences: Derived functors

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Transfer of Model Structures

Covers the transfer of model structures through adjunctions in the context of model categories.

Homotopy Category of a Model Category

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

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.

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.

Why Quasicategories?

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

Serre model structure: Left and right homotopy

Explores the Serre model structure, focusing on left and right homotopy equivalences.

Construction of the homotopy category

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

Homotopy Categories: Model Structures

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

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.

Natural Transformations in Algebra

Explores natural transformations in algebra, defining functors and isomorphisms.