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From this may be abstracted a form of composition, <math>P \circeq Q,</math> where <math>P ~\subseteq~ X \times M</math> and <math>Q ~\subseteq~ M \times Y</math> are otherwise arbitrary dyadic relations, and where <math>P \circeq Q ~\subseteq~ X \times Y</math> is defined as follows:

From this may be abstracted a way of composing two dyadic relations that have a domain in common.  For example, let <math>P \subseteq X \times M</math> and <math>Q \subseteq M \times Y</math> be dyadic relations that have the middle domain <math>M\!</math> in common.  Then we may define a form of composition, notated <math>P \circeq Q,</math> where <math>P \circeq Q ~\subseteq~ X \times Y</math> is defined as follows:

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