# Elementary diagram in institutions

- We generalise the method of diagrams from conventional model theory
to a simple institution-independent (i.e. independent of the details of the
actual logic or institution) framework based on a novel categorical concept
of elementary diagram of a model.

We illustrate the power of our institution-independent method of elementary
diagrams by developing several applications to institution liberality, institution-independent
quasi-varieties, and limits and colimits of theory models.

The results obtained are illustrated systematically with examples from four
different algebraic specification logics. In the introduction we also discuss
the relevance of our institution-independent approach to the model theory
of algebraic specification and computing science, but also to conventional
and abstract model theory.

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