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Applied Category Theory for Engineering I
Last Updated: 2026-06-03 00:07:39
Abstract
Applied Category Theory is an exciting multidisciplinary field of research which harnesses the mathematical language of category theory for applications across a broad range of disciplines. This course is a gentle introduction to this mathematical theory, emphasizing applications in engineering and the “compositional approach” to systems analysis, co-design, and computation.
Objective
Students will be able to: 1) Recognize, understand, and use basic concepts from algebra and category theory. 2) Understand, use, and analyze basic mathematical argumentation and proof-writing (a key tool for using category theory). 3) Name and understand example cases of applied category theory, for instance involving dynamical systems, databases, and complex system co-design (e.g. in the context of autonomous vehicles). 4) Understand the “compositional way of thinking” as a methodological approach to systems analysis, co-design, and computation.
Content
Review of basic algebraic structures [sets, relations, (semi)groups, monoids, actions, order theory] Gentle introduction to category theory [series and parallel composition, feedback, functors, natural transformations, and more...] Many simple applied examples illustrating concepts along the way. Extended examples from dynamical systems, databases, and systems co-design in engineering.
Resources
Lecture Notes
A slides book and a (work-in-progress) textbook for the course will be provided (A. Censi, J. Lorand, G. Zardini, "Applied Compositional Thinking for Engineers").
Literature
Censi, Lorand, Zardini, "Categories and Compositionality, with a view to applications" ( https://tinyurl.com/579kw5bh ). See also https://lorand.earth/act for many additional materials
General Information
- Language
- English
- Levels
- DR , MSC
- Frequency
- Yearly recurring
Examination
- Type
- graded semester performance
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Applied Category Theory for Engineering I | No time listed | 3 h weekly |
Offered In
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Core Courses (The Core Courses in the Master’s program Mechanical Engineering listed below are indicative and include courses designed by the Department at the Master's level. With the approval of the tutor, students may also select Master's-level courses offered by other departments at ETH. These courses will be marked as non-regular in the LAG, but their categorization as Core Courses is possible if included in the approved LAG.)
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Doctorate Mechanical and Process Engineering (More Information at: )