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@dgb37 haha, sounds like you rediscovered the tripos-to-topos construction! That one uses partial equivalence relations and functional relations between them.
@jonmsterling @MartinEscardo @zwarich
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@jonasfrey@mathstodon.xyz
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@jonmsterling What are the three notions of setoids that you have in mind? I've come across the word many times, and was never quite sure what people meant by it.
@MartinEscardo @zwarich
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@johncarlosbaez@mathstodon.xyz So it the picture wrong or am I misinterpreting it ? Maybe the Hubble radius dot is close to the "black hole line", but not quite on it ? Would a universe with a big-cruch singularity in the future (that people used to believe in) be a black hole ? Or does the line capture the correct notion of black hole only for not-too-large objects ? Or is it about universe vs observable universe ?
(I have watched the video and remember the discussion of white holes, but my understanding of all this is superficial)
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@johncarlosbaez@mathstodon.xyz
the universe fits the profile of a white hole a lot better than of a black hole.
Yes, because of the singularity in the past ? But if there also was a singularity in the future then it could be a black hole ?
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@dougmerritt@mathstodon.xyz @johncarlosbaez@mathstodon.xyz on the other hand, the whole universe is a black hole! (The Hubble radius dot in the graphic)
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@dgb37 I'm just saying it's an analogy. The tttc uses p.e.r.s internal to an indexed poset. But not over a "fixed" set in any sense I would say.
@jonmsterling @MartinEscardo @zwarich