Applied Category Theory Course: Ordered Sets

My applied category theory course based on Fong and Spivak’s book Seven Sketches is going well. Over 250 people have registered for the course, which allows them to ask question and discuss things. But even if you don’t register you can read my “lectures”.

We study the applications to logic—both classical logic based on subsets, and a nonstandard version of logic based on partitions. And we show how this math can be used to understand “generative effects”: situations where the whole is more than the sum of its parts. But the real payoff comes in Chapter 2, where we discuss “resource theories”.

• Lecture 1 – Introduction
• Lecture 2 – What is Applied Category Theory?
• Lecture 3 – Chapter 1: Preorders
• Lecture 4 – Chapter 1: Galois Connections
• Lecture 5 – Chapter 1: Galois Connections
• Lecture 6 – Chapter 1: Computing Adjoints
• Lecture 7 – Chapter 1: Logic
• Lecture 8 – Chapter 1: The Logic of Subsets
• Lecture 9 – Chapter 1: Adjoints and the Logic of Subsets
• Lecture 10 – Chapter 1: The Logic of Partitions
• Lecture 11 – Chapter 1: The Poset of Partitions
• Lecture 12 – Chapter 1: Generative Effects
• Lecture 13 – Chapter 1: Pulling Back Partitions
• Lecture 14 – Chapter 1: Adjoints, Joins and Meets
• Lecture 15 – Chapter 1: Preserving Joins and Meets
• Lecture 16 – Chapter 1: The Adjoint Functor Theorem for Posets
• Lecture 17 – Chapter 1: The Grand Synthesis

If you want to discuss these things, please visit the Azimuth Forum and register! Use your full real name as your username, with no spaces, and use a real working email address. If you don’t, I won’t be able to register you. Your email address will be kept confidential.

I’m finding this course a great excuse to put my thoughts about category theory into a more organized form, and it’s displaced most of the time I used to spend on Google+. That’s what I wanted: the conversations in the course are more interesting!