by Marcello Herreshoff 351 days ago | Scott Garrabrant likes this | link | parent “Self-Reference and Fixed Points: A Discussion and an Extension of Lawvere’s Theorem” by Jorge Soto-Andrade and Francisco J. Varela seems like a potentially relevant result. In particular, they prove a converse Lawvere result in the category of posets (though they mention doing this for $$[0,1]$$ in an unsolved problem.) I’m currently reading through this and related papers with an eye to adapting their construction to $$[0, 1]$$ (I think you can’t just use it straight-forwardly because even though you can build a reflexive domain with a retract to an arbitrary poset, the paper uses a different notion of continuity for posets.)

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