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In category theory, a branch of mathematics, a subfunctor is a special type of functor which is an analogue of a subset. ==Definition== Let C be a category, and let ''F'' be a functor from C to the category of sets Set. A functor ''G'' from C to Set is a subfunctor of ''F'' if # For all objects ''c'' of C, ''G''(''c'') ⊆ ''F''(''c''), and # For all arrows ''f'':''c''′→''c'' of C, ''G''(''f'') is the restriction of ''F''(''f'') to ''G''(''c''′). This relation is often written as ''G'' ⊆ ''F''. For example, let 1 be the category with a single object and a single arrow. A functor ''F'':1→Set maps the unique object of 1 to some set ''S'' and the unique identity arrow of 1 to the identity function 1''S'' on ''S''. A subfunctor ''G'' of ''F'' maps the unique object of 1 to a subset ''T'' of ''S'' and maps the unique identity arrow to the identity function 1''T'' on ''T''. Notice that 1''T'' is the restriction of 1''S'' to ''T''. Consequently, subfunctors of ''F'' correspond to subsets of ''S''. 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「Subfunctor」の詳細全文を読む スポンサード リンク
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