; TeX output 2001.12.11:13337 V6N cmbx12MathematischesInstitutmWS2001/026derUniversitXatM`unchenSet86Prof.Dr.B.Pareigis;KNff cmbx12ProblemffsetforAdvancedffAlgebra=}BXQ cmr12(29)\$Let!", cmsy10F:TC!X!uSet,HObSeacorvXariantrepresentablefunctorandlet\$g cmmi12fQ:URM6!N7bSeBSamonomorphisminC5.ShorwthatF1(fG):F(M@)\$^ݯ!n3F1(N@)isamonomorphism,toSo.ʍB(30)`(a)tPLet}fU:OAb/ !*\ӹSet?+bSetheunderlyingfunctor.ShorwthattPU+isarepresenrtablefunctor.`(b)tPShorwpPthatF:( msbm10Qo-VVec3V7!U@(Q22cmmi8n \D )ppmsbm8Q lVp)2SetispPatPrepresenrtablefunctor.B(31)\$ShorwգthatthefunctorFc:URAb3URM67!U@(Z=(n) ZU M)UR2Set|is\$notrepresenrtable(fornUR2).B(32)\$FVore aK-algebraAletA2 K cmsy8 %denotethemrultiplicativee groupof\$elemenrtsthatareinvertibleunderthemultiplicationofA.TLet\$U6:URGrt!%oSet9abSe,theunderlyingfunctor.Shorwthatthefunctor\$Fc:URKo-Alg'3A7!U@(A2)2Setisarepresenrtablefunctor.=}6Duedate:8TVuesdary,11.12.2001,16:15inLectureHall138*;7 )ppmsbm8( msbm10 K cmsy8!", cmsy102cmmi8g cmmi12Nff cmbx12N cmbx12XQ cmr12