{"id":702,"date":"2015-06-30T17:04:52","date_gmt":"2015-06-30T15:04:52","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=702"},"modified":"2017-10-30T17:09:29","modified_gmt":"2017-10-30T16:09:29","slug":"powerdomains-and-hyperspaces-iv-theories","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=702","title":{"rendered":"Powerdomains and hyperspaces IV: theories"},"content":{"rendered":"<p>Last time, we concluded with a mysterious observation. \u00a0There is a theory, that of\u00a0unital\u00a0inflationary topological semi-lattices, which plays a fundamental role in the study of the Hoare powerspace. \u00a0On the one hand,\u00a0<strong>H<\/strong>(X) is the free sober such thing. \u00a0On the other hand, the algebras of the\u00a0<strong>H<\/strong>\u00a0monad are exactly those things that are sober. \u00a0We shall investigate that by looking at theories themselves, and show how those constructions arise from a logical perspective. \u00a0In the end, this turned out to be more complicated than what I had thought initially&#8230; \u00a0<a title=\"Powerdomains and hyperspaces IV: theories\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=664\">Read more.<\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Last time, we concluded with a mysterious observation. \u00a0There is a theory, that of\u00a0unital\u00a0inflationary topological semi-lattices, which plays a fundamental role in the study of the Hoare powerspace. \u00a0On the one hand,\u00a0H(X) is the free sober such thing. \u00a0On the &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=702\">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":[],"class_list":["post-702","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\/702","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=702"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/702\/revisions"}],"predecessor-version":[{"id":1291,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/702\/revisions\/1291"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=702"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=702"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}