Simplicial and Cosimplicial Objects: Examples and Applications

Related lectures (32)

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

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

Introduces the theory of categories through examples and discusses the product of categories.

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

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

Introduces the basics of group theory, defining groups, categories, and groupoids.

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

Covers the construction and universal properties of pushouts in group theory.

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Explores natural transformations between functors in different categories and their applications.

Explores the construction of G-sets and left adjoint functors in category theory.

Page 2 of 2