{"id":5715,"date":"2022-09-19T16:26:39","date_gmt":"2022-09-19T14:26:39","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5715"},"modified":"2023-02-20T19:22:13","modified_gmt":"2023-02-20T18:22:13","slug":"algebras-of-filter-related-monad-ii-kz-monads","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5715","title":{"rendered":"Algebras of filter-related monads: II. KZ-monads"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Alan Day and Oswald Wyler once proved that the algebras of the filter monad on the category&nbsp;<strong>Top<sub>0<\/sub><\/strong>&nbsp;of T<sub>0<\/sub>&nbsp;topological spaces are exactly the continuous (complete) lattices. Mart\u00edn Escard\u00f3 later gave a very interesting proof of this fact, using a category-theoretic construction due to Anders Kock which he calls&nbsp;<em>KZ-monads<\/em>. My purpose is to talk about Escard\u00f3\u2019s argument; but mostly, really, to put forward his notion of KZ-monad, which is a true categorical gem.  Read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=5656\" data-type=\"page\" data-id=\"5656\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alan Day and Oswald Wyler once proved that the algebras of the filter monad on the category&nbsp;Top0&nbsp;of T0&nbsp;topological spaces are exactly the continuous (complete) lattices. Mart\u00edn Escard\u00f3 later gave a very interesting proof of this fact, using a category-theoretic construction &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=5715\">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":[20,21,22,19],"class_list":["post-5715","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-algebra","tag-continuous-lattice","tag-filter","tag-monad"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5715","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=5715"}],"version-history":[{"count":3,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5715\/revisions"}],"predecessor-version":[{"id":5722,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/5715\/revisions\/5722"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}