Vipul at 12:28, 25 December 2008

2008-12-25T12:28:36Z

← Older revision		Revision as of 12:28, 25 December 2008
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	An object in a category is termed a '''zero object''' if it is both an [[defining ingredient::initial object]] and a [[defining ingredient::final object]].		An object in a category is termed a '''zero object''' if it is both an [[defining ingredient::initial object]] and a [[defining ingredient::final object]].

			==Examples==

			===Examples of categories with a zero object===

			* The [[category of groups]] has a zero object: the trivial group. This is both an initial and a final object.
			* The [[category of pointed sets]] has a zero object: a one-point set. This is both an initial and a final object.

			===Examples of categories without a zero object===

			* The [[category of sets]] has no zero object. This is because the initial object (the empty set) is not isomorphic to the final object (the one-point set).
			* The [[category of topological spaces]] has no zero object. This is because the initial object (the empty topological space) is not isomorphic to the final object (the one-point topological space).
			* The [[category of fields]] has neither an initial object nor a final object. Hence, it has no zero object.

			==Related notions==

			* [[Initial object]]
			* [[Final object]]

Vipul: New page: ==Definition== An object in a category is termed a '''zero object''' if it is both an defining ingredient::initial object and a defining ingredient::final object.

2008-12-09T01:24:43Z

New page: ==Definition== An object in a category is termed a '''zero object''' if it is both an defining ingredient::initial object and a defining ingredient::final object.

New page

==Definition==

An object in a category is termed a '''zero object''' if it is both an [[defining ingredient::initial object]] and a [[defining ingredient::final object]].

Zero object - Revision history

Vipul at 12:28, 25 December 2008

Vipul: New page: ==Definition== An object in a category is termed a '''zero object''' if it is both an defining ingredient::initial object and a defining ingredient::final object.