Functorial Semantics

Functorial semantics is a mathematical framework that describes how abstract structures, called theories, relate to concrete interpretations or models. Think of it as a way to systematically map the ideas in a theory to actual systems or data, preserving their relationships. This mapping is called a "functor," which ensures that the connections and operations in the theory are maintained in the interpretation. Essentially, functorial semantics formalizes how theories can be represented and understood through different models, allowing us to study their properties and applications in a consistent, structured way across various fields like computer science, linguistics, and mathematics.