Uploaded September 2026 | Updated September 2026, 2 weeks ago

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Topos Institute Colloquium, 17th of September 2026.
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Classical model theory studies elementary classes which are classes of
models of first-order theories and elementary embeddings between them.
The pursuit of abstract model theory led to Shelah's abstract elementary
classes consisting of models and embeddings satisfying conditions
similar to those satisfied by an elementary class. Abstract elementary
classes are examples of accessible categories whose morphisms are
monomorphisms. We will show that there is a "model theory" of such
accessible categories. Cardinalities of underlying sets of models are
replaced by internal sizes, (Galois) types by equivalence classes of
cospans and independence is understood as a calculus of commuting
squares. These concepts are necessary for a stability theory. We will
also present an unexpected connection of independence with dagger
categories.