Lecture

Homotopical Algebra: The Homotopy Category of a Model Category

Related lectures (40)
Acyclic Models: Cup Product and Cohomology
Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.
Natural Transformations in Algebra
Explores natural transformations in algebra, defining functors and isomorphisms.
Construction of the homotopy category
Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.
The Whitehead Lemma: Homotopy Equivalence in Model Categories
Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.
Elementary Properties of Model Categories
Covers the elementary properties of model categories, emphasizing the duality between fibrations and cofibrations.
Derived functors: Identity and Homotopy Categories
Explores derived functors in model categories, focusing on identity and homotopy categories.
The Topological Künneth Theorem
Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.
Homotopy theory of chain complexes
Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.
Categories and Functors
Explores building categories from graphs and the encoding of information by functors.
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.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.