{"id":3402,"date":"2013-07-24T15:52:35","date_gmt":"2013-07-24T15:52:35","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3402"},"modified":"2013-07-24T15:52:35","modified_gmt":"2013-07-24T15:52:35","slug":"lemma-of-the-day-16","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3402","title":{"rendered":"Lemma of the day"},"content":{"rendered":"<p>Let R &#8212;> A and R &#8212;> B be ring maps. In general there does not exist a functor T : D(B) &#8212;> D(B &otimes;<sub>R<\/sub> A) of triangulated categories such that a B-module M gives an object T(M) of D(B &otimes;<sub>R<\/sub> A) which maps to M &otimes;<sup>L<\/sup><sub>R<\/sub> A under the map D(B &otimes;<sub>R<\/sub> A) &#8212;> D(A). See <a href=\"http:\/\/stacks.math.columbia.edu\/tag\/08J2\">Tag 08J2<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let R &#8212;> A and R &#8212;> B be ring maps. In general there does not exist a functor T : D(B) &#8212;> D(B &otimes;R A) of triangulated categories such that a B-module M gives an object T(M) of D(B &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3402\">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-3402","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\/3402","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=3402"}],"version-history":[{"count":3,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3402\/revisions"}],"predecessor-version":[{"id":3405,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3402\/revisions\/3405"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}