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.
Please give
feedback here, including information about typos, as well as your
comments, questions, and suggestions!
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.
