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 $f, g: x \to y$.

$\array{
x
&
\underoverset
{\underset{g}{\longrightarrow}}
{\overset{f}{\longrightarrow}}
{}
&
y
}$

This may 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.)

**shapes of free diagrams and the names of their limits/colimits**

Revised on May 6, 2017 04:46:20
by Urs Schreiber
(92.218.150.85)