Category Theory for Programmers

These are my notes taken from the video lessons by Bartosz Milewski about Category Theory for Programmers. You can find the videos in Youtube:

Part 1

• Motivation and Philosophy
• What is a category?
• Functions, epimorphisms
• Monomorphisms, simple types
• Examples of categories, orders, monoids
• Kleisli category
• Terminal and initial objects
• Products
• Coproducts, sum types
• Algebraic data types
• Functors
• Functors in programming
• Functoriality, bifunctors
• Monoidal categories, Functoriality of ADTs, Profunctors
• Function objects, exponentials
• Type algebra, Curry-Howard-Lambek isomorphism
• Natural transformations
• Bicategories
• Monads
• Monoid in the category of endofunctors

Part 2

• Declarative vs. Imperative
• Limits
• Limits, Higher order functors
• Limits, Naturality
• Examples of Limits and Colimits
• Free Monoids
• Representable Functors
• Yoneda Lemma
• Yoneda Embedding
• Adjunctions
• Examples of Adjunctions
• Free-Forgetful Adjunctions, Monads from Adjunctions
• Comonads
• Comonads categorically and examples
• F-Algebras, Lambek's Lemma
• Catamorphisms and Anamorphisms
• Lenses
• Lenses categorically