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151-9905-00L 4 Credits DR , MSC D-ITET , D-MAVT , D-INFK
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Applied Category Theory for Engineering I

Lecturers & Examiners: Dr. Jonathan Lorand
Note: The previous course title until HS22 "Applied Compositional Thinking for Engineers II"
VVZ CR n/a

Last Updated: 2026-06-01 11:30:57

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. Homework will consist of weekly homework exercises to check one’s understanding of core mathematical concepts and practice working with the theory (writing mathematical computations and proofs). Homework will constitute 100% of the grade (no exam).

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

Learning Materials (Links)

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
  • Mon 12:15-14:00 (ML F 38)
  • Tue 13:15-14:00 (ML F 38)
3 h weekly

Offered In