OtherEncodingsOfCT.MD

Encoding of Category Theory by Sjoerd Visscher in Haskell

• Category

• Functor

• Domain (source category)

• Codomain (target category)

• Diagonal functor for products

• Codiagonal functor for coproducts

• Void Category

• Adjunction

• Constant Functor

• Identity Functor

• Hom Functor Hom(--,--)

• Covariant functor Hom(X,--)

• Contravariant functor Hom(--,X)

• Star

• Costar

• Directed coproduct category of categories c1 and c2

• Exponential

• Cartesian Closed Category

• Natural transformation

• Component of Natural transformation

• Category of endofunctors

• Category of Presheaves

• Cateory of Profunctors

• Functor composition

• Composition of endofunctors

• Apply Bifunctor

• Postcompose

• Precompose

• Representable

• Initial universal property

• Terminal universal property

• MonoidObject

• ComonoidObject

• Monad

• Comonad

• Tensor Product

• Unit

• Comma Category

• Limit

• Colimit

• Initial Object

• Terminal Object

• Binary Product

• Binary Coproduct

• Cone

• Fixed point category

• Omega category

• 2-categoy (Boolean category)

• category of (F,G)-dialgebras and (F,G)-homomorphisms

• (F,G)-dialgebra

• (F,G)-homomorphism

• Initial F-algebra (initial object in the category of F-algebras)

• Terminal F-coalgebra (terminal object in the category of F-coalgebras)

• Catamorphism of an F-algebra (arrow to it from the initial F-algebra)

• Anamorphism of an F-coalgebra (arrow from it to the terminal F-coalgebra)

• Free algebra of the Monad

• Forgetful functor algebra

• Eilenberg–Moore

Encoding of Category Theory by Stephen Dhal

• Monads Made Difficult - Stephen Diehl (blog post) Category as first class concept, Functors between them, up to Monads, Kleisli Category, IO and List Monad