From mboxrd@z Thu Jan 1 00:00:00 1970 X-Received: by 10.46.33.31 with SMTP id h31mr920078ljh.4.1466102522547; Thu, 16 Jun 2016 11:42:02 -0700 (PDT) X-BeenThere: homotopytypetheory@googlegroups.com Received: by 10.28.215.21 with SMTP id o21ls436282wmg.33.gmail; Thu, 16 Jun 2016 11:42:01 -0700 (PDT) X-Received: by 10.194.216.10 with SMTP id om10mr914077wjc.3.1466102521874; Thu, 16 Jun 2016 11:42:01 -0700 (PDT) Return-Path: Received: from mail-lf0-x22c.google.com (mail-lf0-x22c.google.com. [2a00:1450:4010:c07::22c]) by gmr-mx.google.com with ESMTPS id ur4si1110237lbc.0.2016.06.16.11.42.01 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Thu, 16 Jun 2016 11:42:01 -0700 (PDT) Received-SPF: pass (google.com: domain of ericf...@gmail.com designates 2a00:1450:4010:c07::22c as permitted sender) client-ip=2a00:1450:4010:c07::22c; Authentication-Results: gmr-mx.google.com; dkim=pass head...@gmail.com; spf=pass (google.com: domain of ericf...@gmail.com designates 2a00:1450:4010:c07::22c as permitted sender) smtp.mailfrom=ericf...@gmail.com; dmarc=pass (p=NONE dis=NONE) header.from=gmail.com Received: by mail-lf0-x22c.google.com with SMTP id l188so43755017lfe.2 for ; Thu, 16 Jun 2016 11:42:01 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:references:in-reply-to:from:date:message-id:subject:to :cc; bh=D89xi4PQStK1zDX9Wj+OxNvLSHrE6gyxGRte/K+hbFU=; b=oXqPW/NeaoAmr04qGmu0l4f8MPTvBPvzKXb9UCePkwpqbzo07bvQhr9LiSHoygsSx4 3gN0wdd5mJAq/bEkQTSpexa6dsfAQX0lRI19/Ib+UGy5WATWGlkVmz+7l1BCN9D8sTLL Lkei9fwkH0rjrzMlyQlF16r1EdRBp31M87Qkj+NhkqtByzWTuwusNsGKV7c4UuDIj2ED 8CAjyXa4br9hjOhH+QW/RxvA+tNYoP4vt/MUFlS3JKUPmx/PIYOhsEa+pttupef5ngAg sFlbbZ1yUWvyaVoDEfeAf8XYC1K4iQTdApRXiY9GE6+Mg6AgAGL/vijwjcpn4nUd2F+w 83ew== X-Gm-Message-State: ALyK8tIEChol8IdMoPr/rILcmMLfnA/IQz1aIqCzGRv2M1VHjXvt9jQClfrNKFKTxFvMemJa26ar8WfaWvX5fQ== X-Received: by 10.25.22.70 with SMTP id m67mr1408738lfi.25.1466102521617; Thu, 16 Jun 2016 11:42:01 -0700 (PDT) MIME-Version: 1.0 References: <8C57894C7413F04A98DDF5629FEC90B138B93747@Pli.gst.uqam.ca> <2850536B-0DB8-4F6D-AB3F-D5C28F6855B4@cmu.edu> <932D947A-BCD6-4B7A-BBB6-86077A70F414@chalmers.se> In-Reply-To: From: Eric Finster Date: Thu, 16 Jun 2016 18:41:51 +0000 Message-ID: Subject: Re: [HoTT] Is synthetic the right word? To: Urs Schreiber Cc: Thierry Coquand , Homotopy Type Theory Content-Type: multipart/alternative; boundary=001a11406e540163ca053569988d --001a11406e540163ca053569988d Content-Type: text/plain; charset=UTF-8 Hi, Thierry: Great! That's really cool! It hadn't occurred to me that cubicaltt had that kind of implication for the model theory. Urs: Thanks for the reference. That's exactly the kind of thing I had in mind. Cheers, Eric On Thu, Jun 16, 2016 at 8:18 PM Urs Schreiber wrote: > > was bad) With this in mind, I guess > > in the remark this would correspond to something like considering the > > "enriched" > > presheaves with some chosen model structure. But I'm getting a bit out > of > > my depth here > > so maybe someone can chime in to help me out ... > > The model structure that you are after here, for excisive functors, > modeled on the pointed topologically enriched category of finite > pointed CW-complex is discussed in > > Michael Mandell, Peter May, Stefan Schwede, Brooke Shipley, > "Model categories of diagram spectra" > https://ncatlab.org/nlab/show/Model+categories+of+diagram+spectra > > This is the topologically enriched version of Lydakis' simplicially > enriched model structure for excisive functors > > https://ncatlab.org/nlab/show/model+structure+for+excisive+functors > --001a11406e540163ca053569988d Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Hi,

Thierry: =C2=A0Great!=C2=A0 That= 9;s really cool!=C2=A0 It hadn't occurred to me that cubicaltt had that= kind of implication for the model theory.

Urs: = =C2=A0Thanks for the reference.=C2=A0 That's exactly the kind of thing = I had in mind.

Cheers,

Er= ic

On Thu, Jun 1= 6, 2016 at 8:18 PM Urs Schreiber <urs.sc...@googlemail.com> wrote:
> was bad)=C2=A0 With this in mind, I guess
> in the remark this would correspond to something like considering the<= br> > "enriched"
> presheaves with some chosen model structure.=C2=A0 But I'm getting= a bit out of
> my depth here
> so maybe someone can chime in to help me out ...

The model structure that you are after here, for excisive functors,
modeled on the pointed topologically enriched category of finite
pointed CW-complex is discussed in

Michael Mandell, Peter May, Stefan Schwede, Brooke Shipley,
"Model categories of diagram spectra"
https://ncatlab.org/nlab/show/Model= +categories+of+diagram+spectra

This is the topologically enriched version of Lydakis' simplicially
enriched model structure for excisive functors

https://ncatlab.org/nlab/show/mod= el+structure+for+excisive+functors
--001a11406e540163ca053569988d--