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151-9905-00L 4 Credits DR , MSC D-ITET , D-MAVT , D-INFK
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Applied Compositional Thinking for Engineers II

Lecturers & Examiners: Dr. Andrea Censi, Dr. Jonathan Lorand
VVZ CR n/a

Last Updated: 2026-02-05 16:02:03

Abstract

This course is an introduction to advanced topics in Applied Category Theory focused on the needs of applications. The course favors a computational, constructive, and compositional approach targeted to applications in engineering.

Objective

In many domains of engineering and applied sciences, it would be beneficial to think explicitly about abstraction and compositionality, to improve both the understanding of problems and the design of solutions. Applied Category Theory is a field of mathematics that can help in thinking about precisely such topics. A problem, however, is that this type of mathematics is not traditionally taught -- to date, there exists no easy path for engineers to learn category theory that is approachable and emphasizes engineering applications. This course will fill this gap, extending the efforts proposed in the first part of the class (ACT4E I). This course's goal is not to teach category theory for the sake of it, but to teach the "compositional way of thinking". Category theory will just be the means towards this end. This implies that the presentation of materials sometimes diverges from the usual way to teach category theory, and some common concepts might be de-emphasized in favor of more obscure concepts that are more useful for applications. The applications shown in the class will be mainly in the domains of autonomous robotics and mobility.

Content

Categories Functors Co-design problems Natural transformations Adjunctions Traced monoidal categories Computation: - From mathematical models to algorithms - Solving finite co-design problems - Monads - Modeling uncertainty Enriched category theory: - Profunctors - Enriched categories - Negative category theory Operads Linear logic and resources

Resources

Lecture Notes

Slides and notes will be provided.

Literature

B. Fong, D.I. Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory ( https://arxiv.org/pdf/1803.05316 ) Censi, Lorand, Zardini, Applied Compositional Thinking for Engineers ( https://bit.ly/3qQNrdR )

Learning Materials (Links)

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 150 minutes
Aids
Open book exam
Grade percentage:- 50%: a final written exam- 50%: compulsory continuous performance assessmentThe compulsory continuous performance assessment tasks need not be passed on its own; it is awarded a grade which counts proportionally towards the total course unit grade.If a student does not submit any of the work for the compulsory continuous performance assessment tasks, then for this part of the performance assessment they will receive the grade “1”.

Course Components

Type Title Time & Place Hours
lecture with exercise Applied Compositional Thinking for Engineers II
  • Mon 12:15-14:00 (ML F 38)
  • Tue 13:15-14:00 (ML F 38)
3 h weekly

Offered In