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| In [[category theory]], a branch of mathematics, a [[subcategory]] <math>\mathcal{A}</math> of a [[Category (mathematics)|category]] <math>\mathcal{B}</math> is said to be '''isomorphism-closed''' or '''replete''' if every <math>\mathcal{B}</math>-[[isomorphism]] <math>h:A\to B</math> with <math>A\in\mathcal{A}</math> belongs to <math>\mathcal{A}.</math> This implies that both <math>B</math> and <math>h^{-1}:B\to A</math> belong to <math>\mathcal{A}</math> as well.
| | 33 years old Botanist Winfred Baucum from Nepean, likes boardgames, como [http://www.comoganhardinheiro101.com/inicio/ ganhar dinheiro] na internet and urban exploration. In the previous year has completed a visit to Roskilde Cathedral. |
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| A subcategory which is isomorphism-closed and [[full subcategory|full]] is called '''strictly full'''. In the case of full subcategories it is sufficient to check that every <math>\mathcal{B}</math>-object which is isomorphic to an <math>\mathcal{A}</math>-object is also an <math>\mathcal{A}</math>-object.
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| This condition is very natural. E.g. in the [[category of topological spaces]] one usually studies properties which are invariant under [[homeomorphism]]s – so called [[topological property|topological properties]]. Every topological property corresponds to a strictly full subcategory of <math>\mathbf{Top}.</math>
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| {{PlanetMath attribution|id=8112|title=Isomorphism-closed subcategory}}
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| [[Category:Category theory]]
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Latest revision as of 09:43, 12 January 2015
33 years old Botanist Winfred Baucum from Nepean, likes boardgames, como ganhar dinheiro na internet and urban exploration. In the previous year has completed a visit to Roskilde Cathedral.