Course Overview: Category Theory has become an increasingly popular topic of study mainly due to its unmatched ability to organise and layer abstractions of all sorts and to find commonalities between seemingly unrelated structures. Aside from its appeal to the mathematical community, it has also branched out into science, informatics and industry. This reading course aims to give a taste of a number of advanced Category Theoretic concepts using simple but powerful examples that have been chosen to be representative and at the same time illustrate concrete real world examples from a diversity of scenarios such as electrical circuits, database theory, control theory, signal flow graphs, collaborative design, resource theories and more. The course gives an introduction to monoidal categories and preorders, enrichment, colimits, profunctors, (decorated) cospans, PROPs and operads and aims to relate each technical construct to a real world application rather than giving a comprehensive treatment of any of the listed topics.
Learning Outcomes: The students should get an insight into what it feels like to work with category theoretic structures as well as an idea about how such structures can show up in practice.
Course Synopsis: The course is based on the book ‘Seven Sketches in Compositionality: An Invitation to Applied Category Theory’ by Brendan Fong and David Spivak, freely available at http://www.dspivak.net/7sketches.pdf