{"id":3348,"date":"2013-07-10T06:27:38","date_gmt":"2013-07-10T06:27:38","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3348"},"modified":"2013-07-10T06:27:38","modified_gmt":"2013-07-10T06:27:38","slug":"lemma-of-the-day-9","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3348","title":{"rendered":"Lemma of the day"},"content":{"rendered":"

Let A be a Grothendieck abelian category. Then<\/p>\n

    \n
  1. D(A) has both direct sums and products,<\/li>\n
  2. direct sums are obtained by taking termwise direct sums of any complexes,<\/li>\n
  3. products are obtained by taking termwise products of K-injective complexes.<\/li>\n<\/ol>\n

    See Tag 07D9<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Let A be a Grothendieck abelian category. Then D(A) has both direct sums and products, direct sums are obtained by taking termwise direct sums of any complexes, products are obtained by taking termwise products of K-injective complexes. See Tag 07D9.<\/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-3348","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\/3348","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=3348"}],"version-history":[{"count":3,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3348\/revisions"}],"predecessor-version":[{"id":3351,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3348\/revisions\/3351"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3348"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3348"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}