I assume you mean a proof inside of type theory? This is Exercise 9.6
in the book; I don't know offhand of anywhere that the proof is
written out. You do need to assume the groupoids are
saturated/univalent ("groupoids" in the terminology of the book rather
than "pregroupoids").
On Wed, Feb 20, 2019 at 3:08 AM <kristian.alfsvag@uib.no> wrote:
>
> Hi
>
> I was wondering whether there exists a proof in literature that the type of 1-truncated types is equivalent to the type of groupoids (defined as categories with only isomorphisms, for example).
>
> I.e. a truncated version of the "types as infinity categories" viewpoint.
>
> Thanks in advance,
> Kristian Alfsvåg
>
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