{"id":4205,"date":"2021-09-22T20:13:32","date_gmt":"2021-09-22T18:13:32","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4205"},"modified":"2023-04-20T21:46:05","modified_gmt":"2023-04-20T19:46:05","slug":"topological-functors-i-definition-duality-limits-and-colimits","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4205","title":{"rendered":"Topological functors I: definition, duality, limits and colimits"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">I have briefly mentioned topological functors in a recent post.  It is time for me to explain what they are.  This is a truly wonderful concept, which abstracts topological spaces away and concentrates on the key properties of the forgetful functor from <strong>Top<\/strong> to <strong>Set<\/strong>.  In other words, that forgetful functor is topological, but there are many others, including some involving streams, prestreams, and d-spaces.  We will see some of the classical properties of topological functors, notably that topological functors are self-dual, and that they preserve and create both limits and colimits.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=4133\" data-type=\"page\" data-id=\"4133\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have briefly mentioned topological functors in a recent post. It is time for me to explain what they are. This is a truly wonderful concept, which abstracts topological spaces away and concentrates on the key properties of the forgetful &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=4205\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","footnotes":""},"categories":[1],"tags":[71,39],"class_list":["post-4205","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-category-theory","tag-topological-functor"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4205","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4205"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4205\/revisions"}],"predecessor-version":[{"id":4206,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/4205\/revisions\/4206"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}