nLab
interpretation

Contents

Idea

In formal logic and model theory, interpretation refers to equipping the syntax of some theory with a semantics.

Specifically in the context of categorical logic given a theory TT then an interpretation for it in some category 𝒞\mathcal{C} is a functor Syn(T)𝒞Syn(T) \longrightarrow \mathcal{C} from the syntactic category of TT to 𝒞\mathcal{C} and preserving some relevant structure, such as limits. (See also at algebraic theory and algebra over an algebraic theory for more on this.

References

Revised on March 1, 2014 11:00:13 by Urs Schreiber (82.113.99.155)