Brendan Fong, Postdoc, Department of Mathematics
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Jan/14 | Mon | 02:00PM-03:00PM | 4-237 |
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Jan/15 | Tue | 02:00PM-03:00PM | 4-237 |
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Jan/16 | Wed | 02:00PM-03:00PM | 4-237 |
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Jan/17 | Thu | 02:00PM-03:00PM | 4-237 |
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Jan/18 | Fri | 02:00PM-03:00PM | 4-237 |
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Jan/22 | Tue | 02:00PM-03:00PM | 4-237 |
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Jan/23 | Wed | 02:00PM-03:00PM | 4-237 |
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Jan/24 | Thu | 02:00PM-03:00PM | 4-237 |
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Jan/25 | Fri | 02:00PM-03:00PM | 4-237 |
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Jan/28 | Mon | 02:00PM-03:00PM | 4-237 |
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Jan/29 | Tue | 02:00PM-03:00PM | 4-237 |
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Jan/30 | Wed | 02:00PM-03:00PM | 4-237 |
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Jan/31 | Thu | 02:00PM-03:00PM | 4-237 |
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Feb/01 | Fri | 02:00PM-03:00PM | 4-237 |
Enrollment: Unlimited: No advance sign-up
Attendance: Participants welcome at individual sessions
Prereq: None
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 provide an introductory tour of category theory, with a viewpoint toward modelling real-world phenomena. The course will begin with the notion of poset, and introduce central categorical ideas such as functor, natural transformation, (co)limit, adjunction, the adjoint functor theorem, and the Yoneda lemma in that context. We'll then move to enriched categories, profunctors, monoidal categories, operads, and toposes. Applications to resource theory, databases, codesign, signal flow graphs, and dynamical systems will help ground these notions, providing motivation and a touchstone for intuition. The aim of the course is to provide an overview of the breadth of research in applied category, so as to invite further study.
The course text will be An Invitation to Applied Category Theory; a preprint is freely available here. We will spend two lectures on each chapter.
MIT students may also take this course for credit as 18.S097. Further information available here.
Contact: Brendan Fong, 2-180, bfo@mit.edu