Lectures related to Homotopical Algebra: (Co)Limits

Explores natural transformations in algebra, defining functors and isomorphisms.

Explores homotopical algebra, covering colimits, limits, adjunctions, and their applications in group theory.

Introduces left and right derived functors in homotopical algebra, emphasizing their uniqueness and providing an illustrative example.

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

Explores (co)limits in functor categories and simplicial sets, including equalizers and coequalizers of simplicial maps.

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

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Introduces limits and colimits in a category, covering their properties and uniqueness.

Explores functors between categories and the conditions for left and right adjoints.

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.