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Theories of presheaf type

2004
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Journal of Symbolic Logic (JSL)
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Let us say that a geometric theory T is of presheaf type if its classifying topos is (equivalent to) a presheaf topos. (We adhere to the convention that geometric logic allows arbitrary disjunctions, while coherent logic means geometric and finitary.) Write Mod(T) for the category of Set-models and homomorphisms of T. The next proposition is well known; see, for example, MacLane–Moerdijk [13], pp. 381-386, and the textbook of Adámek–Rosický [1] for additional information: Proposition 0.1. For a

doi:10.2178/jsl/1096901776
fatcat:lrgmk3vkarbpdk6jp6v6r2ox3a