Title of the course: A double-dimensional approach to category theory
Instructor: Asst. Prof. Roald Koudenburg
Institution: METU NCC
Dates: 20-24 July 2020
Prerequisites: Basic abstract algebra
Level: Graduate, Advanced undergraduate (beginning Undergraduate if you’re feeling curious.)
Abstract:
We’ll introduce some introductory and intermediate topics in category theory from the point of view of double categories. In a double category one considers two types of morphisms between objects, instead of the usual single type. E.g. besides functions between sets one also considers relations, and besides homomorphisms between rings one also considers bimodules. One of the advantages of this point of view is that it offers easy generalisations of classical category theory to that of enriched and internal categories.
Topics: functions and relations between sets (locally thin double categories), vertically trivial double categories (monoidal categories of sets, abelian groups), double categories (matrices, spans), monoids and bimodules (ordered sets, rings, categories, double categories, enriched categories, internal categories), Kan extension (optimised functions, (co)limits, adjunctions, enriched/internal Kan extension), Yoneda embeddings (if time permits).
Language: EN