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String diagram : ウィキペディア英語版
String diagram
In category theory, string diagrams are a way of representing 2-cells in 2-categories.
== Definition ==

The idea is to represent structures of dimension ''d'' by structures of dimension ''2-d'', using the Poincaré duality. Thus,
* an object is represented by a portion of plane,
* a 1-cell f:A\to B is represented by a vertical segment — called a ''string'' — separating the plane in two (the left part corresponding to ''A'' and the right one to ''B''),
* a 2-cell \alpha:f\Rightarrow g:A\to B is represented by an intersection of strings (the strings corresponding to ''f'' above the link, the strings corresponding to ''g'' below the link).
The parallel composition of 2-cells corresponds to the horizontal juxtaposition of diagrams and the sequential composition to the vertical juxtaposition of diagrams.


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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