{"id":5647,"date":"2022-08-20T09:52:09","date_gmt":"2022-08-20T07:52:09","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5647"},"modified":"2023-02-20T19:21:33","modified_gmt":"2023-02-20T18:21:33","slug":"algebras-of-the-filter-related-monads-i-ultrafilters-and-manes-theorem","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5647","title":{"rendered":"Algebras of filter-related monads: I. Ultrafilters and Manes&#8217; theorem"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In 1969, Ernest Manes proved the following remarkable result: the algebras of the ultrafilter monad on <strong>Set<\/strong> are exactly the compact Hausdorff spaces.  This is remarkable, because it gives a purely algebraic\/category-theoretic of the otherwise purely topological notion of compact Hausdorff spaces.  I will explain how this is proved, and I will give a few pointers to some extension results of the same kind.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=5575\" data-type=\"page\" data-id=\"5575\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In 1969, Ernest Manes proved the following remarkable result: the algebras of the ultrafilter monad on Set are exactly the compact Hausdorff spaces. This is remarkable, because it gives a purely algebraic\/category-theoretic of the otherwise purely topological notion of compact &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5647\">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":{"footnotes":""},"categories":[1],"tags":[20,17,22,19],"class_list":["post-5647","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-algebra","tag-compactness","tag-filter","tag-monad"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5647","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=5647"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5647\/revisions"}],"predecessor-version":[{"id":5654,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5647\/revisions\/5654"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}