Contents

category theory

# Contents

## Idea

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.

## Limits and colimits

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

Last revised on May 6, 2017 at 04:46:20. See the history of this page for a list of all contributions to it.