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      <div><b>Speaker:</b> Atabey Kaygun- Istanbul Teknik Üniversitesi</div>
      <div><strong>Date:</strong> Wednesday, 16 October 2024 </div>
      <div><strong>Time:</strong> 15:00 - 16:00 </div>
      <div><strong>Location:</strong> Galatasaray Üniversitesi, Ortaköy,
        Çırağan Cd. No:36, 34349 Beşiktaş - H304<br>
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        <div><font size="4"><b
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">Title:</b><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;"> Distributive Laws and Cross Simplicial Groups</span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">Abstract: There is a way of writing an algebraic structure</span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">(a group or an algebra or a category) as a product of two substructures. </span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">This is known as a distributive law, and also as a factorization system. After giving examples, </span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">I am going to introduce crossed simplicial groups. Crossed simplicial groups are defined by a distributive law between the </span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">simplicial category  $\Delta$  and a suitable collection of groups. My main aim is to </span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">explain how one can extend the notion of 'simplicial homotopy' to crossed simplicial </span><br
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;"><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">groups. We'll end with a very interesting example coming from Leibniz algebras that are </span><br
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style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">non-skew-symmet</span><span
style="color: rgb(0, 0, 0); font-family: monospace; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; white-space: pre; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; display: inline !important; float: none;">ric analogues of Lie algebras.</span></font><wbr
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          <p><strong>Note:</strong></p>
          <ul>
            <li>To access the complete seminar calendar please visit
              <a class="moz-txt-link-freetext" href="https://matematik.gsu.edu.tr/tr/arastirma/seminerler">https://matematik.gsu.edu.tr/tr/arastirma/seminerler</a><br>
              and to add to your calendar use <a
href="https://calendar.google.com/calendar/ical/mathseminar%40galatasaray.education/public/basic.ics"
                target="_blank" moz-do-not-send="true">ical url.</a></li>
            <li>Participants from outside Galatasaray Üniversitesi are
              kindly requested to send an email to
              <a class="moz-txt-link-abbreviated" href="mailto:mathseminar@galatasaray.education">mathseminar@galatasaray.education</a> before 13:00 on the day
              of the seminar.</li>
          </ul>
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        <div>Galatasaray Üniversitesi Matematik Bölümü<br>
          <a href="https://matematik.gsu.edu.tr/" moz-do-not-send="true"
            class="moz-txt-link-freetext">https://matematik.gsu.edu.tr/</a><br>
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