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Elements correspondence for instances of models #239

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epatters opened this issue Nov 3, 2024 · 0 comments
Open

Elements correspondence for instances of models #239

epatters opened this issue Nov 3, 2024 · 0 comments
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math Development of background mathematics

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@epatters
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epatters commented Nov 3, 2024

The category of elements construction establishes a correspondence between copresheaves and discrete opfibrations over a category.

This classical correspondence should arise as a special case (for the trivial double theory) of an elements construction establishing a correspondence between instances of a fixed model of a double theory and "discrete opfibrations" over that model. In hand-written notes, I've sketched the elements construction for instances of a model of an arbitrary double theory; however, the corresponding notion of discrete opfibration needs to be identified and then the correspondence needs to proved.

This work would continue #175 and could be the starting point for a paper about modules/instances of models.

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math Development of background mathematics
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