MathDB5 problems
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Escardó–Simpson conjecture on the localic unit interval
Escardó–Simpson conjecture. The localic unit interval should be an interval object in the category of locales.
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The non-implication of discrete infinity from the localic Axiom of Infinity
The discussion concerns an axiomatic approach to locale theory in which a proposed Axiom of Infinity for locales is symmetric under open/proper duality. In this setting, the non-im…
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The conjecture on constructing the patch via Scott continuous nuclei
Patch construction conjecture. It should be possible to use this approach to construct the patch of locales with small bases as the frame of Scott continuous nuclei.
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The spectrum conjecture for the double-powerlocale monad
Spectrum conjecture. There is a natural isomorphism
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The barycentric-subdivision conjecture for localic simplices
A simplex is the localic analogue of the interval, with its vertices as distinguished points, and infinite sequences can be used to represent points through successive subdivisions…