151-9904-00L Applied Category Theory for Engineering II
| Semester | Spring Semester 2024 |
| Lecturers | A. Censi, J. Lorand |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| Comment | Note: The previous course title until FS23 "Applied Compositional Thinking for Engineers I" |
| Abstract | This course is an introduction to advanced topics in Applied Category Theory focused on concepts beyond basic category theory and on the needs of applications. The course favors a computational, constructive, and compositional approach targeted to applications in engineering. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning 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 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Slides and notes will be provided. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Censi, Lorand, Zardini, "Applied Compositional Thinking for Engineers" (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) Censi, Lorand, Zardini, Applied Compositional Thinking for Engineers (https://bit.ly/3qQNrdR) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | There will be no exam; there will be weekly theory homework sheets, and these will constitute the grade for the course. The course is essentially self-contained and can be taken, in principle, without ACT4E I. We assume this preliminary knowledge: 1) Basics of logic & mathematical thinking, ability to write mathematical proofs. 2) Basic algebra (sets, posets, relations, semigroups, groups). Students who took the course Applied Category Theory for Engineering I in the Fall Semester are sufficiently proficient in (1) and (2). | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Competencies |
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