群范畴中的自由对象及其生成元集

A free object and its generators set in group category

通过构造群范畴中任一非空集合上的自由对象F ,即若l:X →F是包含映射 ,G是群 ,f :X→G是集合映射 ,则存在唯一的群同态 f :F →G ,使得 fl =f ,并且证明了若对于i:X →F ,F为群范畴中X上的自由对象 ,则i(X)是群F的生成元集合 .

A free object F of every set X in group category,is given that is,if l:x→F is a map,G is a group, f:x→G is a map between sets then there exists only a homomorphic of groups f :F→G,,satisfing fl=f, if F is a free object of X on i:X→F in group category,then i(x) is generators sets of group F.