Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
started bracket type, just for completeness, but don’t really have time for it
had the chance to add a bit more to bracket type: now there is an Idea-section a Semantics-section.
I have also added links to bracket type to relevant entries, in particular to types and logic - table.
Experts please check. I am pretty sure I know what I am talking about here, but I may not be using language in the standard way.
I am somewhat surprised that the idea of “bracket types” is not already in the original articles on propositions as types. I had thought that taking bracket types is implicitly understood all along.
I have added to bracket type a brief section Definition in homotopy type theory with the definition of $supp(A)$.
Also added four references on this. I see in Mike’s lectures the construction is attributed to Lumsdaine. However in the recent post by Brunerie, it seems to be attributed to Voevodsky. I don’t know. The entry currently does not cite Lumsdaine yet, but probably it should.
Voevodsky defined it, as Guillaume said, “using impredicative quantification and resizing rules” (and also univalence). I believe his definition simply mimics the classical proof that a (1-)topos is a regular category — univalence plus a resizing rule is just the way that you get a subobject classifier in HoTT.
The definition as an HIT is what is due to Peter Lumsdaine.
I added the recursion principle for $supp(A)$. I also added to the notations for the bracket type. We’re up to 6 now.
1 to 8 of 8