▁Ab , ▁the ▁category ▁of ▁ab elian ▁groups , ▁with ▁the ▁group ▁of ▁integers ▁Z ▁serving ▁as ▁the ▁unit . ▁For ▁any ▁commut ative ▁ring ▁R , ▁the ▁category ▁of ▁R - al gebras ▁is ▁mon oid al ▁with ▁the ▁tensor ▁product ▁of ▁al gebras ▁as ▁the ▁product ▁and ▁R ▁as ▁the ▁unit . ▁ ▁The ▁category ▁of ▁pointed ▁spaces ▁( rest rict ed ▁to ▁compact ly ▁generated ▁spaces ▁for ▁example ) ▁is ▁mon oid al ▁with ▁the ▁sm ash ▁product ▁serving ▁as ▁the ▁product ▁and ▁the ▁pointed ▁ 0 - s phere ▁( a ▁two - point ▁discrete ▁space ) ▁serving ▁as ▁the ▁unit . ▁The ▁category ▁of ▁all ▁end of un ctors ▁on ▁a ▁category ▁C ▁is ▁a ▁strict ▁mon oid al ▁category ▁with ▁the ▁composition ▁of ▁fun ctors ▁as ▁the ▁product ▁and ▁the ▁identity ▁fun ctor ▁as ▁the ▁unit . ▁Just ▁like ▁for ▁any ▁category ▁E , ▁the ▁full ▁sub category ▁sp anned ▁by ▁any ▁given ▁object ▁is ▁a ▁mon oid , ▁it ▁is ▁the ▁case ▁that ▁for ▁any ▁ 2 - category ▁E , ▁and ▁any ▁object ▁C ▁in ▁Ob ( E ), ▁the ▁full ▁ 2 - sub category ▁of ▁E ▁sp anned ▁by ▁{ C } ▁is ▁a ▁mon oid al ▁category . ▁In ▁the ▁case ▁E ▁= ▁Cat , ▁we ▁get ▁the ▁end of un ctors ▁example ▁above . ▁▁ ▁B ounded - above ▁meet ▁sem il att ices ▁are ▁strict ▁symmetric ▁mon oid al ▁categories : ▁the ▁product ▁is ▁meet ▁and ▁the ▁identity ▁is ▁the