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・ 2-Mercaptopyridine
・ 2-meter band
・ 2-Methoxy-4-vinylphenol
・ 2-Methoxy-6-polyprenyl-1,4-benzoquinol methylase
・ 2-Methoxyamphetamine
・ 2-Methoxyestradiol
・ 2-Methoxyethanol
・ 2-Butoxyethanol acetate
・ 2-Butyne
・ 2-C-methyl-D-erythritol 2,4-cyclodiphosphate synthase
・ 2-C-methyl-D-erythritol 4-phosphate cytidylyltransferase
・ 2-C-Methyl-D-erythritol-2,4-cyclopyrophosphate
・ 2-C-Methylerythritol 4-phosphate
・ 2-Carbomethoxytropinone
・ 2-Carboxy-D-arabinitol-1-phosphatase
2-category
・ 2-chloro-4-carboxymethylenebut-2-en-1,4-olide isomerase
・ 2-Chloro-9,10-bis(phenylethynyl)anthracene
・ 2-Chloro-9,10-diphenylanthracene
・ 2-Chloro-m-cresol
・ 2-chlorobenzoate 1,2-dioxygenase
・ 2-Chlorobenzoic acid
・ 2-Chlorobutane
・ 2-Chloroethanesulfonyl chloride
・ 2-Chloroethanol
・ 2-Chlorophenol
・ 2-Chloropropionic acid
・ 2-Chloropyridine
・ 2-Chlorostyrene
・ 2-choice hashing


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2-category : ウィキペディア英語版
2-category
In category theory, a 2-category is a category with "morphisms between morphisms"; that is, where each hom-set itself carries the structure of a category. It can be formally defined as a category enriched over Cat (the category of categories and functors, with the monoidal structure given by product of categories).
== Definition ==
A 2-category C consists of:
* A class of ''0-cells'' (or ''objects'') , , ....
* For all objects and , a category \mathbf(A,B). The objects f,g:A\to B of this category are called ''1-cells'' and its morphisms \alpha:f\Rightarrow g are called ''2-cells''; the composition in this category is usually written \circ or \circ_1 and called ''vertical composition'' or ''composition along a 1-cell''.
* For any object  there is a functor from the terminal category (with one object and one arrow) to \mathbf(A,A), that picks out the identity 1-cell  on and its identity 2-cell . In practice these two are often denoted simply by .
* For all objects , and , there is a functor \circ_0 : \mathbf(A,B)\times\mathbf(B,C)\to\mathbf(A,C), called ''horizontal composition'' or ''composition along a 0-cell'', which is associative and admits the identity 1 and 2-cells of as identities. The composition symbol \circ_0 is often omitted, the horizontal composite of 2-cells \alpha:f\Rightarrow g:A\to B and \beta:f'\Rightarrow g':B\to C being written simply as \beta\alpha:f'f\Rightarrow g'g:A\to C.
The notion of 2-category differs from the more general notion of a bicategory in that composition of 1-cells (horizontal composition) is required to be strictly associative, whereas in a bicategory it needs only be associative up to a 2-isomorphism. The axioms of a 2-category are consequences of their definition as Cat-enriched categories:
* Vertical composition is associative and unital, the units being the identity 2-cells .
* Horizontal composition is also (strictly) associative and unital, the units being the identity 2-cells on the identity 1-cells ..
* The interchange law holds; i.e. it is true that for composable 2-cells \alpha,\beta,\gamma,\delta
:(\alpha\circ_0\beta)\circ_1(\gamma\circ_0\delta) = (\alpha\circ_1\gamma)\circ_0(\beta\circ_1\delta)
The interchange law follows from the fact that \circ_0 is a functor between hom categories. It can be drawn as a pasting diagram as follows:
Here the left-hand diagram denotes the vertical composition of horizontal composites, the right-hand diagram denotes the horizontal composition of vertical composites, and the diagram in the centre is the customary representation of both.

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-category」の詳細全文を読む



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