Pointed object

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of a category having a terminal object

A pair where and is a morphism of the terminal object into . An example is a pointed topological space (see Pointed space). The pointed objects of form a category, in which the morphisms are the mappings sending the distinguished point to the distinguished point.


The category of pointed objects of has a zero object (see Null object of a category), namely the terminal object of equipped with its unique point. Conversely, if a category has a zero object, then it is isomorphic to its own category of pointed objects.

How to Cite This Entry:
Pointed object. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article