A¹ homotopy theory

Related lectures (32)

Page 3 of 4

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Explores sets of left homotopy equivalence classes of morphisms in model categories.

Concludes the proof of the existence of left derived functors and discusses total left and right derived functors.

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Explores the homotopy theory of chain complexes, focusing on defining cylinder objects and left homotopy.

Explores the homotopy theory of chain complexes, focusing on retractions and model category structures.