Pointed object

From Encyclopedia of Mathematics
Revision as of 17:36, 22 November 2014 by Richard Pinch (talk | contribs) (links)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

2020 Mathematics Subject Classification: Primary: 18A [MSN][ZBL]

of a category $\mathcal{C}$ having a terminal object

A pair $(X,x_0)$ where $X \in \mathrm{Ob}\,\mathcal{C}$ and $x_0$ is a morphism of the terminal object into $X$. Examples are pointed sets, and pointed topological spaces (see Pointed space). The pointed objects of $\mathcal{C}$ form a category, in which the morphisms are the mappings sending the distinguished point to the distinguished point.


The category of pointed objects of $\mathcal{C}$ has a zero object (see Null object of a category), namely the terminal object of $\mathcal{C}$ equipped with its unique point. Conversely, if a category $\mathcal{C}$ 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