{"id":659,"date":"2015-05-28T11:46:49","date_gmt":"2015-05-28T09:46:49","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=659"},"modified":"2017-10-30T17:09:35","modified_gmt":"2017-10-30T16:09:35","slug":"powerdomains-and-hyperspaces-iii-the-theory-of-h","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=659","title":{"rendered":"Powerdomains and hyperspaces III: the theory of H"},"content":{"rendered":"<p>The last post was late. \u00a0Let me compensate by being early this time.<\/p>\n<p>I had promised you that we would see why the theory of the Hoare powerspace monad was given by a small family of axioms, those of unital inflationary semilattices. \u00a0I will substantiate this claim in two ways. \u00a0Following Andrea Schalk, we shall see that\u00a0<strong>H<\/strong>(<em>X<\/em>) is the free such (sober) thing over\u00a0<em>X<\/em>, and we shall see that those (sober) things are exactly the algebras of the <strong>H<\/strong> monad\u2014a nice way to introduce the notion of algebra of a monad. \u00a0Read the <a title=\"Powerdomains and hyperspaces III: the theory of H\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=605\">full post<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The last post was late. \u00a0Let me compensate by being early this time. I had promised you that we would see why the theory of the Hoare powerspace monad was given by a small family of axioms, those of unital &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=659\">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":[],"class_list":["post-659","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/659","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=659"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/659\/revisions"}],"predecessor-version":[{"id":1292,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/659\/revisions\/1292"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=659"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=659"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}