Introduction to Category Theory (and Categorical Logic) [1 ECTS, SSD: Mat/01]

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.

The minicourse (1 ECTS) will consist of an introduction to category theory (6 hours, the first part) followed by complementary sessions on categorical logic (the second part).

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).

Schedule

• Monday, 01/12/2025 – 10:30–12:30 – Aula T.02a

• Tuesday, 02/12/2025 – 08:30–10:30 – Aula T.02b

• Wednesday, 03/12/2025 – 08:30–11:30 – Aula T.04

• Friday, 05/12/2025 – 16:30–18:30 – Aula T.02b

Venue

Department of Computer Science
University of Verona
Strada le Grazie 15
37134 Verona

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