Category Theory

Postgraduate course

Course description

Objectives and Content

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.

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

Learning Outcomes

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



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



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.

Level of Study


Semester of Instruction

Required Previous Knowledge
For incoming exchange students: At least 60 ECTS in Computer Science and at least 10 ECTS in mathematics.
Recommended Previous Knowledge
Access to the Course
Access to the course requires admission to a programme of study at The Faculty of Mathematics and Natural Sciences.
Teaching and learning methods
Up to 6 hours each week in 13 weeks with lectures and organised laboratory assignments. In addition individual and team exercises and self studies, for a total of 270 study hours.
Compulsory Assignments and Attendance

The compulsory exercises have to be passed.

The assignments are valid two semesters: the semester when they are approved and the succeeding semester.

Forms of Assessment
Oral exam. Compulsory exercises may count towards the final grade. 
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Assessment Semester
Examination both spring semester and autumn semester. In semesters without teaching the examination will be arranged at the beginning of the semester.
Reading List
The reading list will be available within July 1st for the autumn semester and December 1st for the spring semester.
Course Evaluation
The course will be evaluated by the students in accordance with the quality assurance system at UiB and the department.
Examination Support Material
Programme Committee
The Programme Committee is responsible for the content, structure and quality of the study programme and courses.
Course Coordinator
Course coordinator and administrative contact person can be found on Mitt UiB, or contact Student adviser
Course Administrator
The Faculty of Mathematics and Natural Sciences represented by the Department of Informatics is the course administrator for the course and study programme.