parallel morphisms

Two morphisms in a category $C$ are **parallel** if they have the same source and target. Equivalently a pair of **parallel morphisms** in $C$ consists of an object $x$, and object $y$, and two morphisms $f, g: x \to y$.

This can be extended to a family of any number of morphisms, but the morphisms are always compared pairwise to see if they are parallel. Degenerate cases: a family of one parallel morphism is simply a morphism; a family of zero parallel morphisms is simply a pair of objects.

The limit of a pair (or family) or morphisms is called their **equalizer**; the colimit is their **coequalizer**. (Of course, these do not always exist.)

Revised on January 29, 2011 22:04:45
by Toby Bartels
(173.190.146.226)