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[209.85.128.49]) by gmr-mx.google.com with ESMTPS id a4si137561edd.4.2019.02.14.12.06.27 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Thu, 14 Feb 2019 12:06:27 -0800 (PST) Received-SPF: pass (google.com: domain of andrew.m.pitts@gmail.com designates 209.85.128.49 as permitted sender) client-ip=209.85.128.49; Received: by mail-wm1-f49.google.com with SMTP id t200so7370872wmt.0 for ; Thu, 14 Feb 2019 12:06:27 -0800 (PST) X-Received: by 2002:a1c:cf43:: with SMTP id f64mr3155919wmg.61.1550174786496; Thu, 14 Feb 2019 12:06:26 -0800 (PST) MIME-Version: 1.0 References: In-Reply-To: From: Andrew Pitts Date: Thu, 14 Feb 2019 20:06:15 +0000 Message-ID: Subject: Re: [HoTT] A unifying cartesian cubical type theory To: Homotopy Type Theory Cc: Anders Mortberg , "Prof. Andrew M Pitts" Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable X-Original-Sender: andrew.m.pitts@gmail.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of andrew.m.pitts@gmail.com designates 209.85.128.49 as permitted sender) smtp.mailfrom=andrew.m.pitts@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: , On Thu, 14 Feb 2019 at 19:05, Anders Mortberg wr= ote: > The key idea is to weaken the notion of fibration from the cartesian > Kan operations com^r->s so that they are not strictly the identity > when r=3Ds. Instead we introduce weak cartesian Kan operations that are > only the identity function up to a path when r=3Ds. I was interested to read this, because I too use that weakened form of fibration in some work attempting to get a model of univalence based only on composition of paths rather than more general Kan filling operations =E2=80=94 so far unpublished, because I can't quite see = how to get univalent universes to work (but seem frustratingly close to it). Anyway, what I wanted to say is that perhaps one should call these things "Dold fibrations" by analogy with the classic notion of Dold fibration in topological spaces ? Andy --=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.