Applied Category Theory - The Emerging Science of Compositionality

schedule May 14th 12:15 - 12:45 PM place Red Room people 165 Interested

What do programming, quantum physics, chemistry, neuroscience, systems biology, natural language parsing, causality, network theory, game theory, dynamical systems and database theory have in common?

As functional programmers, we know how useful category theory can be for our work - or perhaps how abstruse and distant it can seem. What is less well known is that applying category theory to the real world is an exciting field of study that has really taken off in just the last few years. It turns out that we share something big with other fields and industries - we want to make big things out of little things without everything going to hell! The key is compositionality, the central idea of category theory.

This talk will introduce the emerging field of applied category theory, with the aims of:

  • Giving attendees a broad overview of cutting-edge applications of category theory
  • Building an understanding of a small number of the most important core concepts
  • Getting attendees excited, inspired to learn more, and equipped to apply some basic concepts to their work

 
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Outline/Structure of the Talk

The basic approach is to spend the audience's attention budget wisely on a small number of carefully chosen theoretical concepts, but otherwise leave the audience with a clear motivating picture regardless. Full advantage will be taken of the convenient and intuitive graphical representations that category theory enables, like string diagrams.

Talk structure:

  1. Motivation - what's applied category theory about. Introducing the key concept of compositionality, and string diagrams.
  2. High-level overview of the emerging field of applied category theory; a case-by-case look at some exciting applications, touching briefly on quantum physics, DNA sequencing, US military search & rescue systems, and database migrations. This section will avoid technical details of the different fields, and focus on giving a sense of how category theory relates to what they do.
  3. Teaching selected theoretical concepts: monoidal categories which allow string diagrams, and cospans, operads which allow wiring diagrams. I will probably omit advanced aspects such as weakness/strictness, associators, unitors and the pentagon laws, since they are implicit in string diagrams anyway, and I need the "attention budget" for other stuff. I will also set up wiring diagrams, which seem to be of obvious and immediate utility to programmers. I will use software design as a familiar motivation for both.
  4. Conclusion - why applied category is so exciting. Where to go to learn more, who to follow, what to read.

Learning Outcome

After attending, the audience should:

  • Understand the motivation for the field of applied category theory
  • Have a basic understanding of how it applies to different industries & fields
  • Have a basic theoretical understanding of monoidal categories
  • Be able to use string diagrams and wiring diagrams in their own work designing software
  • Ideally, be as excited as me

Target Audience

Functional programmers

Prerequisites for Attendees

A rudimentary understanding of the basic concepts of category theory will be helpful (but not essential), as I will spend very little time setting up categories and functors. I will assume that the audience are programmers and are familiar with the nature of software development and design.

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