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Commutative diagram
In mathematics, especially the many applications of category theory, a commutative diagram is a diagram of objects and morphisms such that, when picking two objects, one can follow any path through the diagram and obtain the same result by composition.
For example, the first isomorphism theorem is a commutative triangle as follows:
Since f = h o φ, the left diagram is commutative; and since φ = k o f, so is the right diagram.
Similarly, the square above is commutative if y o w = z o x.
Commutativity makes sense for a polygon of any finite number of sides (including just 1 or 2), and a diagram is commutative if every polygonal subdiagram is commutative.
03-10-2013 05:06:04
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details