Lectures related to Introduction to Category Theory: Examples

Covers simplicial and cosimplicial objects in category theory with practical examples.

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

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Explores natural transformations in group theory and category theory, emphasizing functor composition and morphism composition.

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

Provides an overview of categories, functors, and natural transformations in mathematics.

Introduces functors in category theory and explains their composition.

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

Explores examples of categories, morphisms, groupoids, and functors in category theory.

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

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

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

Explores coproducts, universal properties, and natural transformations in category theory.

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

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

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Introduces coproducts in category theory, exploring their properties, universality, and relationships with products.