Category Theory

Objectives:
Category Theory is a mathematical language and a toolbox that can be used for formalizing concepts that arise in our day-to-day activity. It is highly suitable for computer science - it provides sophisticated instruments for modelling and reasoning about complex situations involving structured objects. Category Theory focuses especially on the relations between the objects of interest and on different construction principles for objects.

Content:
The course introduces basic categorical concepts and methods. We focus on applications in programming and modeling.

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student

• is familiar with basic categorical concepts, results, and constructions including category, functor, natural transformation, functor category, slice category, pullback, pushout,
• is familiar with categorical reasoning and is able to prove basic theorems

Skills

The student

• is able to explain those concepts, results, and constructions by examples from informatics,
• has basic capabilities to use category theory to structure and to analyse typical situations in informatics involving complex objects,
• is able to acquire necessary continuative subjects from the literature.

General competence

The student

• can apply his/her knowledge and skills in new areas in order to carry out advanced assignments and projects,
• can communicate extensive independent work and masters language and terminology of the academic field, and
• can communicate about academic issues, analyses and conclusions in the field, both with specialists and the general public.