Introduction to Categories and Categorical Logic

TL;DR

This paper offers an accessible, introductory overview of category theory and categorical logic, aimed at beginners with basic mathematical background, including exercises and references for further study.

Contribution

It provides a beginner-friendly, concise introduction to key concepts in category theory and logic, with minimal prerequisites and practical exercises.

Findings

Clear explanations of fundamental categorical concepts

Practical exercises for self-study

Guidance for further reading and exploration

Abstract

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.