David Spivak and Brendan Fong

Department of Mathematics
Massachusetts Institute of Technology

Office: 2-180
Email: {dspivak, bfo} -- mit/edu

Seven Sketches in Compositionality

An Invitation to Applied Category Theory

General information

Room:Building 2, Room 255
Dates: Tues + Thurs: Jan 9 -- 30  (IAP)
Time: 1:30 -- 3pm
Prerequisites: None

Summary: Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this course, we will give seven sketches on real-world applications of category theory. We will also provide course notes that we hope will become a book.

No prior knowledge of category theory is assumed; we will build up from the basics to the advanced theory over the series of lectures.

Syllabus   Flyer 1   Flyer 2

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Seven Sketches in Compositionality. (Last updated 2018/10/12)

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Videos and other resources

Chapter 1: Cascade effects: posets and adjunctions.
(Video missing)

Chapter 2: Data transformations: categories, functors, universal constructions. For an open source implementation of these ideas, go to Categorical Informatics.
Video: Part 1 and Part 2.

Chapter 3: Resource theories and navigation: Monoidal posets and enrichment.
Video: Part 1, Part 2, and Part 3.

Chapter 4: Collaborative design: Profunctors, categorification, and monoidal categories. For an open-source implementation of these ideas, go to Co-design.science.
Video: Part 1, Part 2

Chapter 5: Signal flow diagrams: Props, presentations, and proofs.
Video Part 1, Part 2, Part 3.

Chapter 6: Electric circuits: hypergraph categories and operads.
Video Part 1, Part 2, Part 3, Part 4, Part 5.

Chapter 7: Logic of behavior: sheaves toposes, and internal languages.
Video Part 1, Part 2, Part 3.

Commons License
This work by David I. Spivak and Brendan Fong is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.