{"id":3278,"date":"2013-06-29T15:48:23","date_gmt":"2013-06-29T15:48:23","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3278"},"modified":"2013-06-29T15:48:23","modified_gmt":"2013-06-29T15:48:23","slug":"lemma-of-the-day-2","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3278","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let (A<sub>n<\/sub>) be an inverse system of abelian groups. The following are equivalent<\/p>\n<ol>\n<li>(A<sub>n<\/sub>) is zero as a pro-object,<\/li>\n<li> lim A<sub>n<\/sub> = 0 and R<sup>1<\/sup>lim A<sub>n<\/sub> = 0 and the same holds for &bigoplus; <sub>i &isin; N<\/sub> (A<sub>n<\/sub>).<\/li>\n<\/ol>\n<p>See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/091C\">Tag 091C<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let (An) be an inverse system of abelian groups. The following are equivalent (An) is zero as a pro-object, lim An = 0 and R1lim An = 0 and the same holds for &bigoplus; i &isin; N (An). See Tag &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3278\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3278","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3278","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3278"}],"version-history":[{"count":9,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3278\/revisions"}],"predecessor-version":[{"id":3298,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3278\/revisions\/3298"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3278"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}