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- W3021736704 abstract "We construct a 2-equivalence $mathfrak{CohTheory}^text{op} simeq mathfrak{TypeSpaceFunc}$. Here $mathfrak{CohTheory}$ is the 2-category of positive theories and $mathfrak{TypeSpaceFunc}$ is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in $mathfrak{CohTheory}$. The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is `the same' as the collection of its type spaces (i.e. its type space functor). In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory. The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories." @default.
- W3021736704 created "2020-05-13" @default.
- W3021736704 creator A5027570928 @default.
- W3021736704 date "2020-05-07" @default.
- W3021736704 modified "2023-09-26" @default.
- W3021736704 title "Type space functors and interpretations in positive logic" @default.
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