I also agree with Mike and Ulrik.

I feel like the example of categories is the perfect opportunity to explain
to
someone who is interested in HoTT *why* there is a version of the
definition
that we prefer, *why* it is different from the notion they may be familiar
with
and *why*, in my humble opinion, it is an improvement.



On Wed, Nov 7, 2018 at 5:56 PM Thorsten Altenkirch <
Thorsten.Altenkirch@nottingham.ac.uk> wrote:

> Sorry, I meant to reply only to Thomas. That explains the language which
> is not the internal language of some category...
>
> T
>
> On 07/11/2018, 16:55, "homotopytypetheory@googlegroups.com on behalf of
> Thorsten Altenkirch" <homotopytypetheory@googlegroups.com on behalf of
> Thorsten.Altenkirch@nottingham.ac.uk> wrote:
>
>     Meinst Du dass die Homs sets sind, oder?
>
>     Man braucht ja nicht, dass die Objekte ein Set sind. Insbesondere
> erlaubt iuns das die Kategorie der Sets zu definieren (also beides klein
> und HSet).
>
>     T.
>
>     On 07/11/2018, 15:36, "homotopytypetheory@googlegroups.com on behalf
> of Thomas Streicher" <homotopytypetheory@googlegroups.com on behalf of
> streicher@mathematik.tu-darmstadt.de> wrote:
>
>         What one calls a category should be a set in the HoTT sense,
>         i.e. validate UIP, but not a set in the sense of size.
>
>         Every deviation from that should be signalled by some adjectives or
>         prefixes. That reflects the practice in category theory.
>
>         Thomas
>
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