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In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products, pullbacks and inverse limits. The dual notion of a colimit generalizes constructions such as disjoint unions, direct sums, coproducts, pushouts and direct limits. Limits and colimits, like the strongly related notions of universal properties and adjoint functors, exist at a high level of abstraction. In order to understand them, it is helpful to first study the specific examples these concepts are meant to generalize. == Definition == Limits and colimits in a category ''C'' are defined by means of diagrams in ''C''. Formally, a diagram of type ''J'' in ''C'' is a functor from ''J'' to ''C'': :''F'' : ''J'' → ''C''. The category ''J'' is thought of as index category, and the diagram ''F'' is thought of as indexing a collection of objects and morphisms in ''C'' patterned on ''J''. One is most often interested in the case where the category ''J'' is a small or even finite category. A diagram is said to be small or finite whenever ''J'' is. 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「Limit (category theory)」の詳細全文を読む スポンサード リンク
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