From mboxrd@z Thu Jan 1 00:00:00 1970 X-Received: by 10.36.50.201 with SMTP id j192mr5154498ita.0.1466101117917; Thu, 16 Jun 2016 11:18:37 -0700 (PDT) X-BeenThere: homotopytypetheory@googlegroups.com Received: by 10.140.38.82 with SMTP id s76ls1879566qgs.61.gmail; Thu, 16 Jun 2016 11:18:37 -0700 (PDT) X-Received: by 10.200.37.170 with SMTP id e39mr4653812qte.20.1466101117459; Thu, 16 Jun 2016 11:18:37 -0700 (PDT) Return-Path: Received: from mail-vk0-x229.google.com (mail-vk0-x229.google.com. [2607:f8b0:400c:c05::229]) by gmr-mx.google.com with ESMTPS id v190si87858vkf.2.2016.06.16.11.18.37 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Thu, 16 Jun 2016 11:18:37 -0700 (PDT) Received-SPF: pass (google.com: domain of urs.sc...@googlemail.com designates 2607:f8b0:400c:c05::229 as permitted sender) client-ip=2607:f8b0:400c:c05::229; Authentication-Results: gmr-mx.google.com; dkim=pass head...@googlemail.com; spf=pass (google.com: domain of urs.sc...@googlemail.com designates 2607:f8b0:400c:c05::229 as permitted sender) smtp.mailfrom=urs.sc...@googlemail.com; dmarc=pass (p=QUARANTINE dis=NONE) header.from=googlemail.com Received: by mail-vk0-x229.google.com with SMTP id d185so84628959vkg.0 for ; Thu, 16 Jun 2016 11:18:37 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlemail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=FfQMMNUYQ683vNuKeiz5euLcF2WZNuud5TmEZZK9GVE=; b=0jlbhUlYbAas6s2dBqFua44cT5VK/HBZhim7YNx/ibS80onDXMUxEvaXkdnUmNVF4v ORnAxFleUOhtG/3OKnZlc2YuR2/D81TMhCQHf80hVecyTN8w4j28/DJ9iULxwZ2yFf3L 88t+yQF4YRdKCUQRsdZc7OglFFFkb8oF2FcKzeeG49UuzbXKlm8qQ2n9GA8pS/JCxSBb tQX/hGSZV38TunoYurZ8jh0pFFCJVfjq5T56x/F31oZXRWoia0wkU+ZUzAK/oAAEbzuB fJ9hFx9B3OPdGTjN0eBr/ypoMQDUlsPInTtCoaRbSuEFQ4cluj7YljS5W2/fs4rSjVrF ATUg== X-Gm-Message-State: ALyK8tJS1vDyRznJtSjRz8FL5h4Gk7IC/51+LciHyalz0MXLB36Q2qHqrCnS4vxYf1SHFE5AgeDLZYA1Mwh2Jg== X-Received: by 10.31.188.80 with SMTP id m77mr2648366vkf.30.1466101117083; Thu, 16 Jun 2016 11:18:37 -0700 (PDT) MIME-Version: 1.0 Received: by 10.103.88.140 with HTTP; Thu, 16 Jun 2016 11:18:36 -0700 (PDT) In-Reply-To: References: <8C57894C7413F04A98DDF5629FEC90B138B93747@Pli.gst.uqam.ca> <2850536B-0DB8-4F6D-AB3F-D5C28F6855B4@cmu.edu> <932D947A-BCD6-4B7A-BBB6-86077A70F414@chalmers.se> From: Urs Schreiber Date: Thu, 16 Jun 2016 20:18:36 +0200 Message-ID: Subject: Re: [HoTT] Is synthetic the right word? To: Eric Finster Cc: Thierry Coquand , Homotopy Type Theory Content-Type: text/plain; charset=UTF-8 > 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