Course Code & Number
CMPE 475
Course Title
Category Theory in Computer Science
Level
BS
Credit Hours/ ECTS Credits
(3+0+0) 3 TEDU Credits, 5 ECTS Credits
Pre-requisite / Co-requisite::
Pre-requisites: NONE
Co-requisites: NONE
Catalog Description
The category of sets and functions. Commutative diagrams. Category theoretic isomorphism. Initial and terminal objects. Monoids. (co) Products. Exponential objects. Cartesian closed categories (CCC). Constructive Logic with natural deduction and its categorical interpretation. Simply typed lambda calculus and its semantics in CCCs. The Curry-Howard-Lambek correspondence. Functors. Contravariance. Functor compositions. Natural transformations. Functor categories. Hom- functors. Adjunctions. Kleisli adjunctions. Eilenberg-Moore adjunctions. Dependent types and their categorical interpretations. The Yoneda lemma. Monads with applications in functional programming.