Homotopical Algebra: (Co)Limits

Related lectures (32)

Page 2 of 4

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

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

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

Introduces the category of simplicial sets and explores the standard n-simplex as a universal example.

Explores how adjunctions relate to limits and colimits, proving their preservation properties.

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

Explores concrete examples of limits and colimits in functors and different categories.

Explores the existence of left derived functors in homotopical algebra, focusing on isomorphism conditions and natural transformations.

Introduces functors, including identity and forgetful functors, and explores duality functors.

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.