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In category theory, a branch of mathematics, a connected category is a category in which, for every two objects ''X'' and ''Y'' there is a finite sequence of objects : with morphisms : or : for each 0 ≤ ''i'' < ''n'' (both directions are allowed in the same sequence). Equivalently, a category ''J'' is connected if each functor from ''J'' to a discrete category is constant. In some cases it is convenient to not consider the empty category to be connected. A stronger notion of connectivity would be to require at least one morphism ''f'' between any pair of objects ''X'' and ''Y''. Clearly, any category which this property is connected in the above sense. A small category is connected if and only if its underlying graph is weakly connected. Each category ''J'' can be written as a disjoint union (or coproduct) of a connected categories, which are called the connected components of ''J''. Each connected component is a full subcategory of ''J''. ==References== * 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「Connected category」の詳細全文を読む スポンサード リンク
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