Theoretical Computer Science for the Working Category Theorist

TL;DR

This paper explores foundational questions in theoretical computer science using category theory, demonstrating how core concepts and theorems can be understood through functoriality and composition across different categories.

Contribution

It introduces a category-theoretic perspective to fundamental concepts in theoretical computer science, simplifying understanding of complex theorems.

Findings

Many theorems follow from functoriality and composition.

Category theory provides a unifying language for core CS concepts.

Surprising simplicity in understanding complex theorems through categories.

Abstract

Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is random?", "What is an algorithm?", etc. We will present many of the major themes and theorems with the basic language of category theory. Surprisingly, many interesting theorems and concepts of theoretical computer science are easy consequences of functoriality and composition when you look at the right categories and functors connecting them.