From: Michael Shulman <firstname.lastname@example.org> To: Valery Isaev <email@example.com> Cc: Jon Sterling <firstname.lastname@example.org>, "HomotopyTypeTheory@googlegroups.com" <email@example.com> Subject: Re: [HoTT] New theorem prover Arend is released Date: Sat, 10 Aug 2019 02:42:12 -0700 Message-ID: <CAOvivQzzLHnq+bXBzkFv3tST0GEUo4f2zmdj025LTaq+EMB7CQ@mail.gmail.com> (raw) In-Reply-To: <CAA520fuU-BEcdg6mrAkTxmqpDhG9pHpD-1a=X7ZU-n8q57dKsg@mail.gmail.com> There is a bit more subtlety here than is evident from the brief description, since everything has to happen in an arbitrary slice category of the model category. But although the slices of a cartesian model category are not in general again cartesian, they are enriched model categories over the base, and so I think I agree that this works since I lives in the base. However, section 2.2 of https://valis.github.io/doc.pdf also appears to assert that an equivalence can be made into a line in the universe for which coercing along the line is *definitionally* equal to the action of the given equivalence, and such that the line associated to the identity equivalence is definitionally constant. The latter seems like it might be obtainable by a lifting property, but I don't immediately see how to obtain the former in a model category? -- 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 HomotopyTypeTheoryfirstname.lastname@example.org. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/CAOvivQzzLHnq%2BbXBzkFv3tST0GEUo4f2zmdj025LTaq%2BEMB7CQ%40mail.gmail.com.
next prev parent reply index Thread overview: 20+ messages / expand[flat|nested] mbox.gz Atom feed top 2019-08-06 22:16 Валерий Исаев 2019-08-07 15:01 ` Andrej Bauer 2019-08-07 22:13 ` Nicolai Kraus 2019-08-08 9:55 ` Valery Isaev 2019-08-10 9:47 ` Michael Shulman 2019-08-10 12:30 ` Valery Isaev 2019-08-10 12:37 ` Valery Isaev 2019-08-08 12:20 ` Jon Sterling 2019-08-08 12:29 ` Bas Spitters 2019-08-08 14:44 ` Valery Isaev 2019-08-08 15:11 ` Jon Sterling 2019-08-08 15:22 ` Valery Isaev 2019-08-10 9:42 ` Michael Shulman [this message] 2019-08-10 12:24 ` Valery Isaev 2019-08-10 23:37 ` Michael Shulman 2019-08-11 10:46 ` Valery Isaev 2019-08-11 12:39 ` Michael Shulman 2019-08-11 16:55 ` Michael Shulman 2019-08-12 14:44 ` Daniel R. Grayson 2019-08-12 17:32 ` Michael Shulman
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