Homotopy theory of chain complexes

Related lectures (32)

Page 3 of 4

Covers two technical lemmas essential for the Fundamental Theorem in homotopical algebra.

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

Explores Quillen equivalences, emphasizing the preservation of cofibrations and acyclic cofibrations.

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.

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

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Delves into homotopical algebra, defining functors and adjunctions with examples.

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

Delves into the computation and geometric realization of small categories, exploring the relationship between nerves and geometric structures.