Franklin's Notes


Category of models

If $\mathscr{L}$ is a first-order language including constant, function, and relation symbols, and $\mathrm{T}$ is a theory over this language, then there is a category $\mathsf{Model}_\mathrm{T}$ whose objects are structures/models satisfying $\mathrm{T}$, and whose morphisms are isomorphisms. Riehl lists several special cases of such categories which are well-known by other names, such as:

category-theory

model-theory

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