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Composition of Mappings

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The composition of two maps $ f:A\to B$ and $ g:B\to C$ is defined by

$\displaystyle a \mapsto (g\circ f)(a) = g(f(a)),\quad a\in A\, , $

which is illustrated in the following diagram:
\includegraphics[width=10cm]{komposition_Bild}





The composition $ \circ$ is associative, i.e.,

$\displaystyle (h\circ g)\circ f = h\circ (g\circ f)\, $

yet it is obviously not commutative.
(Authors: Höllig/Knesch/Abele)
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  automatically generated 5/18/2009