Pointed object
From Encyclopedia of Mathematics
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.
Comments
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: http://encyclopediaofmath.org/index.php?title=Pointed_object&oldid=15650
Pointed object. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pointed_object&oldid=15650
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article