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Added a mentioning of the term logos at the beginning of Heyting category.
Would it be correct to say that a Heyting cateogry is a category for which the Subobject functor is a first-order hyperdoctrine? If so, do we need to require the Beck-Chevalley condition for the adjoint functors or does it follow somehow?
The relevant Beck–Chevalley conditions are satisfied in any regular category, hence also in any Heyting category.
I find it a bit hard to be sure about the type of objects involved (A=>B as morphism), especially since a topos also has connectives from and to products of Omega. Can this be stratified a bit?
Added example: every locally cartesian closed coherent category is a Heyting category.
Anonymous
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