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In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: :hom''C''(''X'', ''X'') = for all objects ''X'' :hom''C''(''X'', ''Y'') = ∅ for all objects ''X'' ≠ ''Y'' Since by axioms, there is always the identity morphism between the same object, we can express the above as condition on the cardinality of the hom-set :| hom''C''(''X'', ''Y'') | is 1 when ''X'' = ''Y'' and 0 when ''X'' is not equal to ''Y''. Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category. == Simple facts == Any class of objects defines a discrete category when augmented with identity maps. Any subcategory of a discrete category is discrete. Also, a category is discrete if and only if all of its subcategories are full. The limit of any functor from a discrete category into another category is called a product, while the colimit is called a coproduct. The functor from Set to Cat that sends a set to the corresponding discrete category is left adjoint to the functor sending a small category to its set of objects. (For the right adjoint, see indiscrete category.) 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「Discrete category」の詳細全文を読む スポンサード リンク
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