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In category theory, a discipline within mathematics, the notion of lax functor between bicategories generalizes that of functors between categories. Let ''C,D'' be bicategories. We denote composition in (diagrammatic order ). A ''lax functor P from C to D'', denoted , consists of the following data: * for each object ''x'' in ''C'', an object ; * for each pair of objects ''x,y ∈ C'' a functor on morphism-categories, ; * for each object ''x∈C'', a 2-morphism in ''D''; * for each triple of objects, ''x,y,z ∈C'', a 2-morphism in ''D'' that is natural in ''f: x→y'' and ''g: y→z''. These must satisfy three commutative diagrams, which record the interaction between left unity, right unity, and associativity between ''C'' and ''D''. See http://ncatlab.org/nlab/show/pseudofunctor. A lax functor in which all of the structure 2-morphisms, i.e. the and above, are invertible is called a pseudofunctor. 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「Lax functor」の詳細全文を読む スポンサード リンク
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