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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 13th 2012
• (edited Sep 13th 2012)

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.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 13th 2012

I have also edited and expanded the Idea section a little. Please check if you can live with this.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeSep 13th 2012

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”.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeSep 14th 2012

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.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeSep 20th 2012

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?

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeSep 20th 2012

Thanks! Very nice and very helpful.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeOct 27th 2017

At h-set there was no mentioning that they form a pretopos. I have added a minimum here.