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<div class="pre" style="margin: 0; padding: 0; font-family: monospace"><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Sayın Matematikçiler,</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Aşağıda FGC-Yüksek Yapılar Seminerleri kapsamında yapılacak konuşmanın detaylarını bulacaksınız. Salı günleri yapılan bu etkinlikleri, bir kereye mahsus olarak bu kez <strong>Perşembe</strong> günü yapacağımızı dikkatinize sunarım.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">İyi çalışmalar,</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">ilhan ikeda</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Dear friends,</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">On the <span style="color: #ba372a;">6th of March 2025 THURSDAY (note the unusual day!)</span> at 18:00 </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Istanbul local time (10:00 Cleveland local time), Juan Orendain from </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Case Western Reserve University will be the speaker of the first talk of </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">the Spring Semester of Feza Gursey Center for Physics and Mathematics </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Higher Structures Research Group Seminars.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">The details of Juan's seminar talk are as follows:</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Speaker:</strong> Juan Orendain (Case Western Reserve University)</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Date:</strong> <span style="color: #ba372a;">March 06, 2025, Thursday (note the unusual day!)</span>.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Time:</strong> 18:00 Istanbul local time (10:00 Cleveland local time)</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Title: </strong><em>Crossed products of decorated bicategories and length of </em></span><em><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">equipments</span></em><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Abstract</strong></span><em><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">:</span></em><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Equipments are categorical structures of dimension 2 having two separate types of 1-arrows -vertical and horizontal- and supporting restriction and extension of horizontal arrows along vertical ones. Equipments are 2-functors satisfying certain conditions, but they can also be understood as double categories satisfying a fibrancy condition. In the zoo of 2-dimensional categorical structures, they fit nicely between 2-categories and double categories, and are generally considered as the 2-dimensional categorical structures where synthetic category theory is done, and in reasonable cases, where monoidal bicategories are more naturally defined.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">In this talk I discuss the problem of lifting a 2-category into an equipment along a given category of vertical arrows, and how this problem allows us to define a notion of length on general double categories. The length of a double category is a number that roughly measures the amount of work one needs to do to reconstruct the double category from a bicategory along its set of vertical arrows. I will review the length of double categories, and I will discuss the crossed product of a decorated bicategory construction -a method for constructing different double categories from a given bicategory is presented-. One of the main ingredients of the construction are so-called canonical squares. I will show that in certain classes of equipments -fully faithful and absolutely dense- every square that can be canonical is indeed canonical. I will explain how from this, it can be concluded that fully faithful and absolutely dense equipments are of length 1, and so they can be 'easily' reconstructed from their horizontal bicategories.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Zoom uygulaması Bilim Akademisi tarafından sağlanmaktadır./Zoom link is provided by The Science Academy.</span><br /><br /><strong><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Zoom link details:</span></strong><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">(As usual the Zoom link will be active 30 minutes before the seminar time; that is at 17:30 Istanbul time/09:30 Cleveland time.)</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Topic:</strong> FGC - Higher Structures Seminars - Spring Term</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><strong>Date and Time:</strong> 06 March 2025 active for the period 17:30-20:00 Istanbul time</span><br /><br /><span style="background-color: #f1c40f;"><strong><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;">Join Zoom link</span></strong></span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><a style="background-color: #f1c40f;" href="https://us02web.zoom.us/j/89763545977?pwd=lYGC8MH3sT6HYT0NSKLvyDkB14K0H7.1" target="_blank" rel="noopener noreferrer">https://us02web.zoom.us/j/89763545977?pwd=lYGC8MH3sT6HYT0NSKLvyDkB14K0H7.1</a></span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><strong>Meeting ID:</strong> 897 6354 5977</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><strong>Passcode:</strong> 467808</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Best regards,</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Ilhan</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Organized by Feza Gürsey Center for Physics and Mathematics</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Supported by Bilim Akademisi - The Science Academy</span></div>
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