Nerve (category theory)

Related lectures (32)

Page 2 of 4

Introduces natural transformations in category theory through concrete examples from group theory.

Covers the concept of simplices in delta complexes and explains the standard n-simplex and the ordering of vertices.

Covers details of the upcoming theoretical exam, including structure and guidelines.

Explores the characterization of limits and colimits as adjoints in category theory.

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Explores the restriction functor in group theory, focusing on its properties.

Explores the concept of free abelian groups as an important left adjoint functor.

Delves into direct sums of abelian groups, showcasing their coproduct properties and universal verification.

Introduces natural transformations in group theory and category theory, emphasizing their definition and significance.

Introduces two fundamental examples of simplicial sets: the nerve of a small category and the singular simplicial set of a topological space.