JRC for Logic
Tsinghua University – University of Amsterdam Joint Research Centre for Logic
JRC for Logic
Tsinghua University – University of Amsterdam Joint Research Centre for Logic

Introduction to Categorical Logic

  • Time: 13:30-16:05, June 23rd-27th
  • Location: Room 4201, Teaching Building No.4 (四教).
  • Lecturer: Ivan Di Liberti (Göteborgs Universitet) and Lingyuan Ye (University of Cambridge) 
  • TA：Zhongqin Gao （gaozq21@mails.tsinghua.edu.cn）
  • Course webpage：Introduction-to-Categorical-Logic
  • A WeChat group has been created for announcements, room changes, and social events. If you haven’t received invitation,  please contact the TA. 

Ivan Di Liberti

 Lingyuan Ye

Course Description

Categorical Logic, and Functorial semantics more specifically, emerged in the 1960s as an alternative framework to capture universal algebra. The framework offers a collection of advantages, including a more flexible and modular approach to semantics, which delivers a perfect correspondence with syntax. These tools offer a more quantitative and conceptual take on completeness results and definability-type theorems.

After a brief introduction to the language of categories, we focus on universal algebra and functorial semantics. We capture the notion of algebraic theory via categories with products (Lawvere theories) and present a syntax-semantics duality between varieties and Lawvere theories. The course ends with some vistas on the theory of sketches which offers a much more general framework, covering the leap from universal algebra to infinitary first order logic.

Tentative Schedule

TBA.

Background Knowledge

The audience is expected to be familiar and have played with the basic definitions of one of following objects: vector space, monoid, group, ring, module, set equipped with operations.

Slides and Exercises

TBA.