Category Theory (CT) is a field of mathematics that explores the relationships and structures between abstract objects. It provides a framework for understanding how different mathematical concepts are connected and how their relationships behave. In category theory:

• Objects represent entities or concepts. These could be numbers, shapes, sets, spaces, or other abstract things.
• Arrows (or morphisms) are the connections or transformations between objects. For example, a function can be an arrow that maps elements from one set to another.
• A category is formed by a collection of objects and arrows that satisfy certain conditions.

Category Theory can be seen as a mathematical toolbox that helps identify common patterns and structures across different areas, from geometry and algebra to computer science and physics. Quantinuum's work on Quantum NLP and Compositional Intelligence and tools such as lambeq are based on the mathematical framework of monoidal categories, exploiting connections and similarities between quantum physics and compositional structures in language.