|
In category theory, a branch of mathematics, a zero morphism is a special kind of morphism exhibiting properties like the morphisms to and from a zero object. ==Definitions== Suppose C is a category, and ''f'' : ''X'' → ''Y'' is a morphism in C. The morphism ''f'' is called a constant morphism (or sometimes left zero morphism) if for any object ''W'' in C and any ''g'', ''h'' : ''W'' → ''X'', ''fg'' = ''fh''. Dually, ''f'' is called a coconstant morphism (or sometimes right zero morphism) if for any object ''Z'' in C and any ''g'', ''h'' : ''Y'' → ''Z'', ''gf'' = ''hf''. A zero morphism is one that is both a constant morphism and a coconstant morphism. A category with zero morphisms is one where, for every two objects ''A'' and ''B'' in C, there is a fixed morphism 0''AB'' : ''A'' → ''B'' such that for all objects ''X'', ''Y'', ''Z'' in C and all morphisms ''f'' : ''Y'' → ''Z'', ''g'' : ''X'' → ''Y'', the following diagram commutes: The morphisms 0''XY'' necessarily are zero morphisms and form a compatible system of zero morphisms. If C is a category with zero morphisms, then the collection of 0''XY'' is unique.〔http://math.stackexchange.com/questions/189818/category-with-zero-morphisms〕 This way of defining a "zero morphism" and the phrase "a category with zero morphisms" separately is unfortunate, but if each homset has a ″zero morphism", then the category "has zero morphisms". 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「zero morphism」の詳細全文を読む スポンサード リンク
|