Doctoral School

Introduction to Category Theory for Non-Mathematicians

Target audience

This course is intended for PhD students, postdoctoral researchers, and (research) master’s students working in philosophy, history and philosophy of science, the arts, the humanities and social sciences, as well as the natural sciences."

Abstract

This course offers a philosophically oriented introduction to category theory. Originating in 1945 as an alternative to set-theoretic foundations, category theory defines mathematical objects not by their internal composition but—consistent with what may be called a structuralist spirit—by the network of relations they maintain with other objects of the same kind. Participants will engage with the key concepts of category theory —categories, functors, natural transformations, limits, colimits, and more—and explore their implications for philosophical debates concerning equality, identity, and difference, as well as the relevance of category theory to mathematical structuralism and to the philosophy of abstraction. Bridging abstract mathematics and philosophical reflection, the course fosters interdisciplinary dialogue across the formal and natural sciences, the humanities and social sciences, and the arts.

Objectives

By the end of this course, participants will be able to:

·      Understand the historical context and mathematical motivations of category theory, as well as the difference between set-theoretic and categorical approaches to mathematical foundations.

·       Grasp the core concepts of category theory: category, functor, natural transformation, and (co)limit.

·       Analyse how category theory reshapes key philosophical notions such as equality, identity, and abstraction.

·       Engage critically with debates concerning the relation between category theory and mathematical structuralism.

·       Read and interpret selected philosophical texts related to category theory.

About the lecturer: Gabriel Catren

Gabriel Catren holds a PhD in Theoretical Physics (University of Buenos Aires) and a PhD in Philosophy (Université Paris 8 Vincennes–Saint-Denis). He is a permanent researcher at SPHERE – Sciences, Philosophie, Histoire (UMR 7219, Université Paris Cité – CNRS). His work lies at the intersection of the philosophy of physics and the philosophy of mathematics, with particular attention to classical and quantum mechanics, gauge theories, category theory, and homotopy type theory. He served as Program Director at the Collège International de Philosophie in Paris from 2007 to 2013 and was Principal Investigator of the ERC-funded project Philosophy of Canonical Quantum Gravity (2011–2017). He has co-directed major international initiatives, including the CNRS International Research Project Identities, Forces, Quanta and The Multiplicity Turn: Theories of Identity From Poetry to Mathematics (France–Stanford Center for Interdisciplinary Studies, Stanford University). Since 2018, he has led the LIFE Project in experimental scientific education at the Performing Arts Forum (PAF) in France.

Dates and venue

13/04/2025: 9h30-12h30 / 14h30-17h30

15/04/2025: 9h30-12h30 / 14h30-17h30

17/04/2025: 9h30-12h30 / 14h30-17h30

Location: Faculty of Arts and Philosophy, Room 2.24, Blandijnberg 2, 9000 Ghent.

Preliminary Programme

  • April 13th 2026

    • General introduction: set-theoretic (extensional) versus category-theoretic (structuralist) foundations of mathematics

    • Definition of a category; examples of categories

    • Kinds of morphisms: monomorphisms, epimorphisms, and isomorphisms

    • Philosophical interpretations of mathematical equality (and, a fortiori, of identity). Isomorphisms as category-theoretical ‘‘stretchings” of the mathematical equality

    • Groupoids as unifying generalizations of sets, equivalence relations, and groups; the ‘‘dialectics of identity and difference

    • Towards higher category theory.

  • April 15th 2026
    • Dual constructions via ‘‘concrete universals''
      • final and initial objects;
      • equalizers and coequalizers
      • products and coproducts;
      • pullbacks and pushouts.
    • Limits and colimits.
  • April 17th 2026.
    • Functors and natural transformations.
    • The category of categories.
    • Natural equivalences as a criterion of identity for categories.
    • Adjoint functors.
    • Representable functors and the Yoneda lemma.

Registration

Registration fee

Registration is free for participants from UGent, KU Leuven and VUB

For other participants, there is a registration fee of 50€.

Coffee and lunch are provided.

Participants need to provide their own accommodation and transports.

Number of participants

Maximum 25

Language

English

Evaluation method

To have the summer school recognized as a specialist course, we expect 15h of attendance and active participation.

After successful participation, the Doctoral School Office will add this course to your curriculum of the Doctoral Training Programme in Oasis. Please note that this can take up to one to two months after completion of the course.

Accommodation suggestions

Budget

Mid-range

Contact us

The organizing team is happy to help you! 

Contact [marjolein.holvoet@ugent.be] for all questions related to the specialized course.