Limits and Colimits: Understanding Categories

Related lectures (32)

Page 3 of 4

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

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

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

Covers group quotient, group actions, and functors connecting sets and G-sets.

Explores natural transformations in algebra, defining functors and isomorphisms.

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

Introduces adjunctions in category theory, exploring necessary conditions and natural transformations for adjoint functors.

Explores identity and forgetful functors in category theory, showcasing their role in preserving structure and relationships between categories.

Introduces functors in category theory and explains their composition.

Explores composition of functors, induced functors, and preservation of commutative diagrams in category theory.