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[2607:f8b0:4864:20::a2f]) by gmr-mx.google.com with ESMTPS id 143si32362vkw.4.2018.11.07.09.33.56 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Wed, 07 Nov 2018 09:33:56 -0800 (PST) Received-SPF: pass (google.com: domain of ericfinster@gmail.com designates 2607:f8b0:4864:20::a2f as permitted sender) client-ip=2607:f8b0:4864:20::a2f; Received: by mail-vk1-xa2f.google.com with SMTP id y14so3899563vkd.1 for ; Wed, 07 Nov 2018 09:33:56 -0800 (PST) X-Received: by 2002:a1f:2145:: with SMTP id h66mr477397vkh.65.1541612036248; Wed, 07 Nov 2018 09:33:56 -0800 (PST) MIME-Version: 1.0 References: <3c553ba0-2181-44ec-b790-969a8115ea1f@googlegroups.com> <1a3288ec-ca0e-48ce-80ad-9cad01f56845@googlegroups.com> <4ae4c745-a00e-4ebd-9de2-e29474b75d48@googlegroups.com> <20181107153556.GC26970@mathematik.tu-darmstadt.de> <25749C08-4CFC-4B16-955E-92E59EF4D180@exmail.nottingham.ac.uk> In-Reply-To: <25749C08-4CFC-4B16-955E-92E59EF4D180@exmail.nottingham.ac.uk> From: Eric Finster Date: Wed, 7 Nov 2018 18:31:11 +0100 Message-ID: Subject: Re: [HoTT] Re: Precategories, Categories and Univalent categories To: Thorsten Altenkirch Cc: Thomas Streicher , Ulrik Buchholtz , Homotopy Type Theory Content-Type: multipart/alternative; boundary="000000000000cd59d6057a168584" X-Original-Sender: ericfinster@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; dkim=pass header.i=@gmail.com header.s=20161025 header.b=YIpMToGC; spf=pass (google.com: domain of ericfinster@gmail.com designates 2607:f8b0:4864:20::a2f as permitted sender) smtp.mailfrom=ericfinster@gmail.com; dmarc=pass (p=NONE sp=QUARANTINE dis=NONE) header.from=gmail.com Precedence: list Mailing-list: list HomotopyTypeTheory@googlegroups.com; contact HomotopyTypeTheory+owners@googlegroups.com List-ID: X-Google-Group-Id: 1041266174716 List-Post: , List-Help: , List-Archive: , --000000000000cd59d6057a168584 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable 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 > > =EF=BB=BFOn 07/11/2018, 16:55, "homotopytypetheory@googlegroups.com on be= half of > Thorsten Altenkirch" 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" 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 > > -- > You received this message because you are subscribed to the Googl= e > Groups "Homotopy Type Theory" group. > To unsubscribe from this group and stop receiving emails from it, > send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. > > > > > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please contact the sender and delete the email and > attachment. > > Any views or opinions expressed by the author of this email do not > necessarily reflect the views of the University of Nottingham. Email > communications with the University of Nottingham may be monitored > where permitted by law. > > > > > -- > You received this message because you are subscribed to the Google > Groups "Homotopy Type Theory" group. > To unsubscribe from this group and stop receiving emails from it, sen= d > an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. > > > > > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please contact the sender and delete the email and > attachment. > > Any views or opinions expressed by the author of this email do not > necessarily reflect the views of the University of Nottingham. Email > communications with the University of Nottingham may be monitored > where permitted by law. > > > > > -- > You received this message because you are subscribed to the Google Groups > "Homotopy Type Theory" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to HomotopyTypeTheory+unsubscribe@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. > --=20 You received this message because you are subscribed to the Google Groups "= Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an e= mail to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. --000000000000cd59d6057a168584 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
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 defini= tion=C2=A0
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 <Tho= rsten.Altenkirch@nottingham.ac.uk> wrote:
Sorry, I meant to reply only to Thomas. That explains the lan= guage which is not the internal language of some category...

T

=EF=BB=BFOn 07/11/2018, 16:55, "homotopytypetheory@googlegroups.com = on behalf of Thorsten Altenkirch" <homotopytypetheory@googlegroups.co= m on behalf of Thorsten.Altenkirch@nottingham.ac.uk> wrote:

=C2=A0 =C2=A0 Meinst Du dass die Homs sets sind, oder?

=C2=A0 =C2=A0 Man braucht ja nicht, dass die Objekte ein Set sind. Insbeson= dere erlaubt iuns das die Kategorie der Sets zu definieren (also beides kle= in und HSet).

=C2=A0 =C2=A0 T.

=C2=A0 =C2=A0 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:

=C2=A0 =C2=A0 =C2=A0 =C2=A0 What one calls a category should be a set in th= e HoTT sense,
=C2=A0 =C2=A0 =C2=A0 =C2=A0 i.e. validate UIP, but not a set in the sense o= f size.

=C2=A0 =C2=A0 =C2=A0 =C2=A0 Every deviation from that should be signalled b= y some adjectives or
=C2=A0 =C2=A0 =C2=A0 =C2=A0 prefixes. That reflects the practice in categor= y theory.

=C2=A0 =C2=A0 =C2=A0 =C2=A0 Thomas

=C2=A0 =C2=A0 =C2=A0 =C2=A0 --
=C2=A0 =C2=A0 =C2=A0 =C2=A0 You received this message because you are subsc= ribed to the Google Groups "Homotopy Type Theory" group.
=C2=A0 =C2=A0 =C2=A0 =C2=A0 To unsubscribe from this group and stop receivi= ng emails from it, send an email to HomotopyTypeTheory+unsubscr= ibe@googlegroups.com.
=C2=A0 =C2=A0 =C2=A0 =C2=A0 For more options, visit https://groups= .google.com/d/optout.





=C2=A0 =C2=A0 This message and any attachment are intended solely for the a= ddressee
=C2=A0 =C2=A0 and may contain confidential information. If you have receive= d this
=C2=A0 =C2=A0 message in error, please contact the sender and delete the em= ail and
=C2=A0 =C2=A0 attachment.

=C2=A0 =C2=A0 Any views or opinions expressed by the author of this email d= o not
=C2=A0 =C2=A0 necessarily reflect the views of the University of Nottingham= . Email
=C2=A0 =C2=A0 communications with the University of Nottingham may be monit= ored
=C2=A0 =C2=A0 where permitted by law.




=C2=A0 =C2=A0 --
=C2=A0 =C2=A0 You received this message because you are subscribed to the G= oogle Groups "Homotopy Type Theory" group.
=C2=A0 =C2=A0 To unsubscribe from this group and stop receiving emails from= it, send an email to HomotopyTypeTheory+unsubscribe@googlegrou= ps.com.
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This message and any attachment are intended solely for the addressee
and may contain confidential information. If you have received this
message in error, please contact the sender and delete the email and
attachment.

Any views or opinions expressed by the author of this email do not
necessarily reflect the views of the University of Nottingham. Email
communications with the University of Nottingham may be monitored
where permitted by law.




--
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