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151-9904-00L 4 Credits DR , MSC D-ITET , D-ARCH , D-BAUG , D-MAVT , D-ERDW , D-INFK , D-PHYS

Applied Category Theory for Engineering II

Lecturers: Dr. Jonathan Lorand

Examiners: Dr. Andrea Censi, Dr. Jonathan Lorand

Note: The previous course title until FS23 "Applied Compositional Thinking for Engineers I"

VVZ CR 3.6

Last Updated: 2026-06-03 00:14:04

Abstract

An introduction to Applied Category Theory at a more advanced level than Part I (this "Part II" is self-contained however). Category theory is increasingly used across a broad range of disciplines, from AI to physics, from linguistics to epidemiology. This course teaches the core mathematical concepts and highlights applications in applied sciences, with a special emphasis on engineering.

Objective

Overall goal: to acquire a basic fluency and ability in category theory, and to understand some examples of how it is applied in engineering and adjacent fields. More specifically, by the end of this course, you will be able to: 1) Recognize, name, differentiate, and connect core concepts of category theory, and be able to use them in proofs and calculations. 1a) State from memory the most important definitions/concepts. 1b) Verify by proof/calculation that a given example fits the definition of a concept X. Perform calculations needed for using a mathematical concept for applications. 1c) State which concepts are special cases of other concepts, and how. Compare and contrast mathematical concepts. 2) Describe and illustrate some principle themes and questions of the “compositional way of thinking” as a methodological approach. 2a) Name some concrete examples where "compositionality" plays a role. 2b) List a number of questions that the topic of "compositionality" addresses. 3) Name and describe a few example cases of category theory being used in applied settings. 3a) Name the mathematical structure involved and how it relates to the application in question. 3b) Explain how general principles come to bear in the given examples.

Content

We will cover the follow topics, and connect them to applications across various disciplines: - Categories - Functors - Universal constructions - Natural transformations, Yoneda - Adjunctions - Monads - Comonads - Monoidal categories - Traced monoidal categories - Bicategories

Resources

Lecture Notes

A textbook and other resources will be provided.

Literature

Censi, Lorand, Zardini, "Categories and Compositionality, with a view to Applications" (Link: https://bit.ly/3qQNrdR ) B. Fong, D.I. Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory ( https://arxiv.org/pdf/1803.05316 )

Learning Materials (Links)

Main link
In-progress texbook

General Information

Language: English
Levels: DR , MSC
Frequency: Yearly recurring

Examination

Type: graded semester performance

The performance assessment for this course is composed of three main parts; the percentages given below indicate their respective weight as part of the total grade for the course:- Graded homework sheets (70%)- Written exam I during the semester (20%)- Written exam II during the semester (10%)The two exams will consist of tasks that are similar to those given in the graded homework sheets. For each of the exams, the only assisting materials allowed are personally handwritten notes that occupy a maximum of five A4-sized pages (your notes may be written on both sides of the pages). In particular, no electronic devices are allowed. The two exams will each be 1.5 hours in duration and will occur during date-time slots that are reserved for this course's lecture sessions (V) or exercise sessions (U). All performance assessments will be in the english language.

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Applied Category Theory for Engineering II	Mon 12:15-14:00 (ML F 39) Wed 12:15-13:00 (ML F 39)	3 h weekly
lecture	Applied Category Theory for Engineering II	Mon 12:15-14:00 (ML F 39)	2 h weekly
exercise	Applied Category Theory for Engineering II	Wed 12:15-13:00 (ML F 39)	1 h weekly

Offered In

Mechanical Engineering Master
- 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.)
Civil Engineering Master
- Electives (The entire course programs of ETH Zurich and the University of Zurich are open to the students to individual selection.)
  - Recommended Electives of Master Programme
Robotics, Systems and Control Master
- Core Courses
Doctorate Mechanical and Process Engineering (More Information at: )
- Subject Specialisation
Integrated Building Systems Master
- Main Courses
  - Specialised Courses
Space Systems Master
- Deep Track Courses (At least 20 credits must be completed within the deep track courses. Surplus credit points can be counted towards the electives.)
  - Robotics
    - Deep Track Robotics (These courses can be credited either as a specialization subject or as an elective subject.)