From mboxrd@z Thu Jan 1 00:00:00 1970 X-Received: by 10.28.55.205 with SMTP id e196mr57243wma.0.1475884262361; Fri, 07 Oct 2016 16:51:02 -0700 (PDT) X-BeenThere: homotopytypetheory@googlegroups.com Received: by 10.25.198.18 with SMTP id w18ls121877lff.44.gmail; Fri, 07 Oct 2016 16:51:01 -0700 (PDT) X-Received: by 10.46.33.101 with SMTP id h98mr1439471ljh.5.1475884261664; Fri, 07 Oct 2016 16:51:01 -0700 (PDT) Return-Path: Received: from sun60.bham.ac.uk (sun60.bham.ac.uk. [147.188.128.137]) by gmr-mx.google.com with ESMTPS id p199si368578wmd.1.2016.10.07.16.51.01 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Fri, 07 Oct 2016 16:51:01 -0700 (PDT) Received-SPF: softfail (google.com: domain of transitioning escardo...@googlemail.com does not designate 147.188.128.137 as permitted sender) client-ip=147.188.128.137; Authentication-Results: gmr-mx.google.com; spf=softfail (google.com: domain of transitioning escardo...@googlemail.com does not designate 147.188.128.137 as permitted sender) smtp.mailfrom=escardo...@googlemail.com; dmarc=fail (p=QUARANTINE dis=QUARANTINE) header.from=googlemail.com Received: from [147.188.128.54] (helo=mailer3) by sun60.bham.ac.uk with esmtp (Exim 4.84) (envelope-from ) id 1bseur-000797-Ns for HomotopyT...@googlegroups.com; Sat, 08 Oct 2016 00:51:01 +0100 Received: from host86-137-209-253.range86-137.btcentralplus.com ([86.137.209.253] helo=[192.168.1.112]) by bham.ac.uk (envelope-from ) with esmtpsa (TLSv1.2:DHE-RSA-AES128-SHA:128) (Exim 4.84) id 1bseur-0002O7-Dz for HomotopyT...@googlegroups.com using interface auth-smtp.bham.ac.uk; Sat, 08 Oct 2016 00:51:01 +0100 Subject: Re: Joyal's version of the notion of equivalence To: "HomotopyT...@googlegroups.com" References: <963893a3-bfdf-d9bd-8961-19bab69e0f7c@googlemail.com> From: Martin Escardo Message-ID: <25c7daf7-8c0f-97de-7d3d-34851bf50a98@googlemail.com> Date: Sat, 8 Oct 2016 00:51:00 +0100 User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.3.0 MIME-Version: 1.0 In-Reply-To: <963893a3-bfdf-d9bd-8961-19bab69e0f7c@googlemail.com> Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-BHAM-SendViaRouter: yes X-BHAM-AUTH-data: TLSv1.2:DHE-RSA-AES128-SHA:128 via 147.188.128.21:465 (escardom) This shouldn't have happened (it seems like a bug): On 08/10/16 00:09, Martin Escardo wrote: > Questions: > > f:X->Y is a Joyal-equivalence := (Sigma(g:Y->X).g.f~id)x(Sigma() > > (1) How I intended to send a complete message to somebody else (did you get it?), but instead it seems somehow we got a double bug: wrong recipient, and 1% of the message. Apologies. I don't know how such a thing can happen. (From Thunderbird.) M.