莆田学院学报
莆田學院學報
보전학원학보
JOURNAL OF PUTIAN UNIVERISTY
2012年
5期
1-4,13
,共5页
三角范畴%Abel化%recollement
三角範疇%Abel化%recollement
삼각범주%Abel화%recollement
triangulated category%Abelian%recollement
首先给出了加法范畴的Abel化与幂等完备化的关系，证明了加法范畴的幂等完备化范畴是其Abel化范畴的投射子范畴；在此基础上，证明了三角范畴recollement的Abel化是Abel范畴的右recollement。
首先給齣瞭加法範疇的Abel化與冪等完備化的關繫，證明瞭加法範疇的冪等完備化範疇是其Abel化範疇的投射子範疇；在此基礎上，證明瞭三角範疇recollement的Abel化是Abel範疇的右recollement。
수선급출료가법범주적Abel화여멱등완비화적관계，증명료가법범주적멱등완비화범주시기Abel화범주적투사자범주；재차기출상，증명료삼각범주recollement적Abel화시Abel범주적우recollement。
The relationship between Abelian and idempotent completion of additive categories was presented in this paper. It proves that the idempotent completion of an additive category is the subcategory of its Abelian category, which consists of all the projectives. Then we prove that the Abelian of a recollement of triangulated categories is a right recollement of Abelian categories.
