CS 680: Category Theory and Applications in Computing

Course Contents:

Introduction: Basic definition and diagram; sources and sinks; monicity and epicity; isomorphisms of objects and morphisms; duality; Universal Structures: Initial terminal and zero; Category of sources and sinks; product; equalizer; regular epicity and monicity; pullback; completeness; kernel; Normal Categories: Normal hierarchy; extension of categories; factorization; chains and exactness; Morphism algebra: Biproduct; semiadditive category; Additive category; Functors: Natural transformation; categories on natural transformation; property preserving and reflecting functors; Diagram isomorphism; Similar categories; generalization of limit and colimit; H-reflection morphism and adjoint functor; Representable functors Category in context of another category; Application to Logic (Topoi); application to Programming Languages.