; TeX output 2001.12.18:10097 V6N cmbx12MathematischesInstitutmWS2001/026derUniversitXatM`unchen#Set106Prof.Dr.B.Pareigis;KNff cmbx12ProblemffsetforAdvancedffAlgebra=}BXQ cmr12(37)\$Letbg cmmi12f;g.:yXkx!", cmsy10 !Y_ҹbSetrwobmaps. Showthatthesetfxy2\$XjfG(x)1=gn9(x)g3nwiththeinclusionmapinrtoX$isanequalizer\$off;gË:URXF``!Yp.ʍB(38)`(a)tPLetthecommrutativediagramM>ō BC 32fd*dO line10-gۍ$gbY6VPbY oA{fd*ά-;W}pH̝rǠ*FfeФǠ? z>qHTǠ*FfeǠ?` :dftPbSeTapullbacrk(alimit)ofthemorphismsfQ: A#!-C1handtPg:$BU!Cܞ.iAssumethatgi'isamonomorphism.ShorwtPthatpisalsoamonomorphism.`(b)tPShorwthatthecategoryofsetshaspullbacks.B(39)\$LetJX;andY慹bSetrwoJsets.W'ShowthatthedisjointunionXO_[Y\$isacoproSductofX+andYinthecategoryofsets.B(40)\$ShorwthatthecategoryofsetshascoSequalizers.Bэ6Duedate:8TVuesdary,8.1.2002,16:15inLectureHall138*;7 !", cmsy10g cmmi12Nff cmbx12N cmbx12XQ cmr12O line10)