Universal properties in double category theory

About this position

Universal properties in double category theory

The objective of this position is to advance the understanding of universal properties in double category theory and to demonstrate applications in theoretical computer science. Topics may include loose universal properties, two-dimensional sketches, double-categorical enrichment, and formal category theory.

The project will address the following key areas:

Double categories provide a unified framework for the study of both functional and relational structure, jointly generalising the classical notions of 2-category and bicategory in two-dimensional category theory. Double category theory is becoming an increasingly useful tool in both mathematics and theoretical computer science, for instance in the development of two-dimensional methods for scientific modelling and in the study of systems theories. However, the general theory of double categories is still nascent, and there remain fundamental questions about the nature of double categories.

The goal of this project is to advance the theory of double categories and to demonstrate applications in theoretical computer science. Depending on the interests and background of the candidate, topics may include loose universal properties, two-dimensional sketches, double-categorical enrichment, and formal category theory. We envision the project to extend the existing theory of 2-categories and bicategories, as well as to develop entirely new methods in study of low-dimensional higher category theory.

Responsibilities and (foreseen) tasks:

• The student’s primary responsibility is research on this PhD project.
• The student may have to contribute to the teaching activities of the lab as a course assistant.

Applicants should fulfil the following requirements:

• A strong knowledge of basic category theory and an interest in theoretical computer science. Applicants from under-represented and diverse backgrounds are particularly encouraged to apply.

The following experience is beneficial:

• Experience in two-dimensional category theory is beneficial.

We offer:

• We offer a fully funded PhD position for 48 months in a vibrant research environment. The gross salary is 2300 EUR/month, which ensures a good living standard in Estonia. The start date is negotiable.

Supervisors:

Main supervisor: Researcher Bryce James Clarke, School of Information Technologies: Department of Software Science: High-assurance Software Laboratory

Co-Supervisor: Researcher Nathanael Amariah Arkor, School of Information Technologies: Department of Software Science: High-assurance Software Laboratory

Tallinn University of Technology (TalTech) is an international scientific community with approximately 9,000 students and 2,000 employees; it is one of the largest universities in Estonia, the leading EU country in digitalisation. The university's strengths are broad multidisciplinary study/research interests, a modern research environment, and strong collaboration with international educational and research institutions. TalTech is aiming to be an organisation leading the way to a sustainable digital future.

The Department of Software Science is a leading computer science department in Estonia. In particular, we are strong in programming language theory, logic, type theory, category theory. The relevant labs are the High-Assurance Software Laboratory, incl the Logic and Semantics Group , and the Lab for Compositional Systems and Methods .

We have a number of PhD students working in these domains, we collaborate with many European centers, receive many visitors.

For information about the admission process, please visit the PhD Admission homepage

Applications can be submitted from 01.10.2026 to 10.11.2026