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2-functors : ウィキペディア英語版
2-functor
In the mathematical field of Category theory, a 2-functor is a morphism between 2-categories. Because strict 2-categories can be defined as categories enriched in ''Cat'', the category of small categories, a 2-functor can be defined succinctly as a ''Cat''-enriched functor.
Spelling this out a bit, let ''C'' and ''D'' be categories. A 2-functor F\colon C\to D consists of
* a function F\colon \text C\to \text D, and
* for each pair of objects c,c'\in C a functor F_\colon \text_(c,c')\to\text_D(Fc,Fc') on hom-categories,
such that these functors strictly preserves identity objects and commute with compositions.
See for more details and for lax versions.
==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「2-functor」の詳細全文を読む



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