Minicourse "Introduction to Category Theory (and Categorical Logic)"

November 14, 2025

Introduction to Category Theory (and Categorical Logic)
Matteo Spadetto (LS2N of the University of Nantes)
December 1–5, 2025

Abstract
Category theory offers a powerful and unifying way to look at mathematics and theoretical computer science. It provides a common language to describe structures and relationships across different areas, from algebra and topology to logic and computation. This course gives an introduction to category theory for master students, combining basic concepts with their (logical) applications.

In the first part, we will cover the main ideas of this subject:

  • Categories, functors, and natural transformations
  • Universal properties and limits
  • Adjunctions

In the second part, we will explore how logic can be interpreted within categories (focusing on the fragment of regular logic and on regular categories):

  • Internal logic and categorical semantics
  • Regular categories and regular theories
  • Completeness

This minicourse aims to build intuition through examples and exercises. By the end, students will have a solid grasp of the categorical way of thinking (and how it connects to logical systems and their semantics).

Note: The minicourse itself (1 ECTS) will consist of the first 6 hours, covering the introduction to category theory (see the first part of the abstract). The remaining hours will be complementary sessions on categorical logic (the second part of the abstract).

Timetable
Monday 1st: 10:30-12:30 - Aula T.02a
Tuesday 2nd: 08:30-10:30 - Aula T.02b
Wednesday 3rd: 08:30-11:30 - Aula T.04
Friday 5th: 16:30-18:30 - Aula T.02b

Page on the University of Verona website
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