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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