Subobject classifier: Difference between revisions

Revision as of 15:49, 4 March 2005

Revision as of 09:36, 9 April 2005

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== Definition ==

For the general definition, we start with a category '''C''' that has a [[terminal object]], which we denote by 1. The object Ω of '''C''' is a subobject classifier for '''C''' if there exists a morphism

:1 ->→ Ω

with the following property:

:for each [[monomorphism]] ''j'': ''U'' ->→ ''X'' there is a unique morphism ''g'': ''X'' -> Ω such that the following [[commutative diagram]]

''U'' -> 1