Applied Category Theory Course: Collaborative Design



Our course on applied category theory is now starting the fourth chapter of Fong and Spivak’s book Seven Sketches. Chapter 4 is about collaborative design: building big projects from smaller parts. This is based on work by Andrea Censi:

• Andrea Censi, A mathematical theory of co-design.

The main mathematical content of this chapter is the theory of enriched profunctors. We’ll mainly talk about enriched profunctors between categories enriched in monoidal preorders. The picture above shows what one of these looks like!

Here are the lectures:

Lecture 55 – Chapter 4: Enriched Profunctors and Collaborative Design
Lecture 56 – Chapter 4: Feasibility Relations
Lecture 57 – Chapter 4: Feasibility Relations
Lecture 58 – Chapter 4: Composing Feasibility Relations
Lecture 59 – Chapter 4: Cost-Enriched Profunctors
Lecture 60 – Chapter 4: Closed Monoidal Preorders
Lecture 61 – Chapter 4: Closed Monoidal Preorders
Lecture 62 – Chapter 4: Constructing Enriched Categories
Lecture 63 – Chapter 4: Composing Enriched Profunctors
Lecture 64 – Chapter 4: The Category of Enriched Profunctors
Lecture 65 – Chapter 4: Collaborative Design
Lecture 66 – Chapter 4: Collaborative Design
Lecture 67 – Chapter 4: Feedback in Collaborative Design
Lecture 68 – Chapter 4: Feedback in Collaborative Design
Lecture 69 – Chapter 4: Feedback in Collaborative Design
Lecture 70 – Chapter 4: Tensoring Enriched Profunctors
Lecture 71 – Chapter 4: Caps and Cups for Enriched Profunctors
Lecture 72 – Chapter 4: Monoidal Categories
Lecture 73 – Chapter 4: String Diagrams and Strictification
Lecture 74 – Chapter 4: Compact Closed Categories
Lecture 75 – Chapter 4: The Grand Synthesis
Lecture 76 – Chapter 4: The Grand Synthesis
Lecture 77 – Chapter 4: The End? No, the Beginning!

One Response to Applied Category Theory Course: Collaborative Design

  1. John Baez says:

    As of today the course is now officially done, though some students may carry on discussing things with me. My classes at U.C.R. are starting up now, and I can’t keep on teaching an extra class just for the fun of it.

    It would have been nice to go on further, but I found it took more and more work to explain things in sufficient detail as the book progressed, so on the whole I am happy to stop here.

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