Sheaves on distributive lattices #671
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mzeuner
reviewed
Dec 16, 2021
| -- TODO: is unique existence expressed like this what we want? We | ||
| -- might have to assume that C is univalent for this to work. | ||
| statement : (F' : DLBasisSheaf) | ||
| → ∃![ F ∈ DLSheaf L C T ] ((x : fst L) → (x ∈ L') → CatIso C (F-ob (fst F) x) (F-ob (fst F') x)) -- TODO: if C is univalent the CatIso could be ≡? |
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This is how I would have understood the statement, so I think that should work.
Regarding the conditions on C I think we need
- that it is univalent
- that it has finite limits (or pullbacks and a terminal object)
isGroupoid (C .ob)
The last point is not strictly necessary, but we have to have some control over the hLevel as we want to writeF(x)in terms of its basis cover which is information hidden under a prop truncation...
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Yeah, I'll add this as a comment
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I'm going to merge this once the CI is done just so that @mzeuner can continue working on it easier |
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Work in progress on sheaves on distributive lattices. Mainly for @mzeuner