Lecture

Categories: Functors, and Natural Transformations

Related lectures (32)

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

Explores natural transformations in algebra, defining functors and isomorphisms.

Explores building categories from graphs and the encoding of information by functors.

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

Explores the concept of category theory, providing examples and discussing the opposite category concept.

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

Explores natural transformations between functors, emphasizing their composition-preserving properties and significance in category theory.

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

Covers the transfer of model structures through adjunctions in the context of model categories.

Covers the concept of isomorphism in categories, defining morphisms with inverses and exploring automorphisms and groupoids.

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

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

Covers adjunctions and functor categories, emphasizing their significance in category theory and applications in deep learning.

Covers the definition and properties of natural transformations between functors in category theory.

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

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

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

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

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

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