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zero object (Definition)

An initial object in a category $\mathcal{C}$ is an object $A$ in $\mathcal{C}$ such that, for every object $X$ in $\mathcal{C}$ there is exactly one morphism $A \longrightarrow X$

A terminal object in a category $\mathcal{C}$ is an object $B$ in $\mathcal{C}$ such that, for every object $X$ in $\mathcal{C}$ there is exactly one morphism $X \longrightarrow B$

A zero object in a category $\mathcal{C}$ is an object $0$ that is both an initial object and a terminal object.

All initial objects (respectively, terminal objects, and zero objects), if they exist, are isomorphic in $\mathcal{C}$




"zero object" is owned by djao.
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Also defines:  initial object, terminal object

Attachments:
examples of initial objects and terminal objects and zero objects (Example) by AxelBoldt
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Cross-references: isomorphic, morphism, object, category
There are 37 references to this entry.

This is version 2 of zero object, born on 2002-04-22, modified 2002-07-11.
Object id is 2864, canonical name is ZeroObject.
Accessed 7658 times total.

Classification:
AMS MSC18A05 (Category theory; homological algebra :: General theory of categories and functors :: Definitions, generalizations)

Pending Errata and Addenda
None.
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Complex analysis - Cauchy's theorem for a rectangle with exceptional points by koundinya on 2005-06-10 08:18:34
Hi all,
 I'm not able to locate the solution to this question - Cauchy's theorem for a rectangle at exceptional points. What are these exceptional points ? Any help on this would be highly appreciated.

TIA

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