A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures

TL;DR

This paper reviews key results in Samson Abramsky's work, emphasizing topological duality, category theory, and their role in unifying logical and computational structures for advancing computer science.

Contribution

It highlights the fundamental role of duality, category theory, and their applications in logic and computer science, providing a comprehensive overview of Abramsky's influential results.

Findings

Topological duality methods solve logic and computer science problems.

Category theory unifies power and structure in computer science.

Landmark results influence current and future research directions.

Abstract

We identify and highlight certain landmark results in Samson Abramsky's work which we believe are fundamental to current developments and future trends. In particular, we focus on the use of (i) topological duality methods to solve problems in logic and computer science; (ii) category theory and, more particularly, free (and co-free) constructions; (iii) these tools to unify the `power' and `structure' strands in computer science.