{"id":2284,"date":"2022-01-27T11:04:29","date_gmt":"2022-01-27T09:04:29","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2284"},"modified":"2022-02-14T12:21:18","modified_gmt":"2022-02-14T10:21:18","slug":"u-haifa-topology-geometry-seminar-sunday-jan-30-2022-speaker-sanjeevi-krishnan-ohio-state-university-title-a-kan-condition-for-directed-homotopy","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2284","title":{"rendered":"U. Haifa Topology &#038; Geometry seminar: Sunday, Jan. 30, 2022. Speaker: Sanjeevi Krishnan (Ohio State University). &#8220;Title:\u00a0 A Kan Condition for Directed Homotopy&#8221;"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>Time: <\/strong>Sunday Jan 30th, 17:00 (Israel Time)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Location: <\/strong>On Zoom<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Speaker: <\/strong>Sanjeevi Krishnan (Ohio State University)<br><strong><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Title:<\/strong> A Kan Condition for Directed Homotopy<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract.<\/strong><br>The Kan condition guarantees that a simplicial set, a formal colimit of abstract simplices, models enough features of a topological space so that classical homotopy theory can be given a completely combinatorial description.&nbsp; There is a similar such Kan condition for cubical sets, formal colimits of abstract hypercubes.&nbsp; &nbsp;We present a generalization of the Kan condition suitable for directed homotopy theory, a homotopy theory for spaces with direction (like spacetimes).&nbsp; &nbsp;Concretely, we present a lifting condition on cubical sets, satisfied by all nerves of small categories, that yields a cubical approximation theorem for directed topology.&nbsp; Intuitively, this condition can be regarded as some kind of weak higher categorical structure on a cubical set.&nbsp; A distinguishing feature of the lifting condition is that it is an algebraic lifting condition [Garner, Grandis, Riehl] in the sense that the lifts have to be suitably natural.&nbsp; One simple application is a cochain-theoretic description of a directed $1$-cohomology theory, represented by directed classifying spaces of commutative monoids.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>ZOOM COORDINATES:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09\">https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Meeting ID: 849 8759 1026<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time: Sunday Jan 30th, 17:00 (Israel Time) Location: On Zoom Speaker: Sanjeevi Krishnan (Ohio State University) Title: A Kan Condition for Directed Homotopy Abstract.The Kan condition guarantees that a simplicial set, a formal colimit of abstract simplices, models enough features&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2284\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,4],"tags":[],"class_list":["post-2284","post","type-post","status-publish","format-standard","hentry","category-gt-seminar","category-seminar"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2284","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2284"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2284\/revisions"}],"predecessor-version":[{"id":2286,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2284\/revisions\/2286"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}