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Prompted by discussion in the thread on “internal sets” (badly named so) I have added to h-set a comment in Properties - Relation to internal set.
I have also edited and expanded the Idea section a little. Please check if you can live with this.
I also disagree with this, for the same reason I mentioned in the other thread. Usually, in homotopy type theory (especially when regarded as the internal language of an $(\infty,1)$-topos) it is the 0-truncated objects which play the role of “sets”.
What shall we do?
I suppose we need to more thoroughly keep qualifiers around. Are we on the safe side with the “n-strictness”-terminology?
Right now I can’t check or do anything, as I have a connection of about one bit per second. But I’ll try to fix later whatever mess I may have created.
I’ve rewritten the section “Relation to internal sets” at h-set from the perspectitve I advocated in the other thread. I don’t have time right now to hash out the right “strict” qualifiers, unfortunately. Can you live with what I wrote for now?
Thanks! Very nice and very helpful.
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