{"id":1654,"date":"2024-04-26T14:39:18","date_gmt":"2024-04-26T19:39:18","guid":{"rendered":"https:\/\/research.knight.domains\/urf\/uncategorized\/morphisms-and-homotopies-in-a-simplicial-setting\/"},"modified":"2024-04-26T14:39:29","modified_gmt":"2024-04-26T19:39:29","slug":"morphisms-and-homotopies-in-a-simplicial-setting","status":"publish","type":"post","link":"https:\/\/research.knight.domains\/urf\/2024-presentations\/morphisms-and-homotopies-in-a-simplicial-setting\/","title":{"rendered":"Morphisms and homotopies in a simplicial setting"},"content":{"rendered":"<p><strong>Sydney Vitalbo<\/strong> Mathematics &amp; Computer Science<br \/>\n<strong>Leah Widlarz<\/strong> Mathematics Education<br \/>\n<strong> <\/strong> <br \/>\n<strong> <\/strong> <\/p>\n<p><strong>Jacob Lauerbacher <\/strong>Associate Professor of Mathematics<br \/>\n<strong> <\/strong> <br \/>\n<strong> <\/strong> <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/research.knight.domains\/urf\/wp-content\/uploads\/2024\/04\/Sydney-Vitalbo-and-Leah-Widlarz-Morphisms-and-Homotopies-in-a-Simplicial-Setting-scaled.jpg\" alt=\"poster\" \/><\/p>\n<h3><a href=\"https:\/\/research.knight.domains\/urf\/wp-content\/uploads\/2024\/04\/Sydney-Vitalbo-and-Leah-Widlarz-Morphisms-and-Homotopies-in-a-Simplicial-Setting-scaled.jpg\">View Poster<\/a><\/h3>\n<p><\/p>\n<h3>Abstract<\/h3>\n<p><\/p>\n<p>We work in a category of simplicial objects that allow us to accommodate a changing module structure in each dimension. In this poster, we present what the morphisms between these objects must look like, as well as how homotopies between them must behave. Among other results, we have verified that the homotopy structure defines an equivalence relation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sydney Vitalbo Mathematics &amp; Computer Science Leah Widlarz Mathematics Education Jacob Lauerbacher Associate Professor of Mathematics View Poster Abstract We work in a category of simplicial objects that allow us to accommodate a changing module structure in each dimension. In this poster, we present what the morphisms between these objects must look like, as well [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":1655,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36],"tags":[30,20],"class_list":["post-1654","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-2024-presentations","tag-natural-science","tag-poster","has-thumbnail"],"_links":{"self":[{"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/posts\/1654","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/comments?post=1654"}],"version-history":[{"count":1,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/posts\/1654\/revisions"}],"predecessor-version":[{"id":1656,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/posts\/1654\/revisions\/1656"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/media\/1655"}],"wp:attachment":[{"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/media?parent=1654"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/categories?post=1654"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/research.knight.domains\/urf\/wp-json\/wp\/v2\/tags?post=1654"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}