A pair groupoid

h is an arrow from a to b in the groupoid, while g is an arrow from b to c. Their composition is gh. The arrow h may be freely varied, while g may only vary on the source fibre through b, in order to obtain a well-defined composition.

The red and blue lines represent the source and target fibres, respectively. The black line represents the identity arrows.

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Brent Pym, 29 August 2013, Created with GeoGebra