Content deleted Content added
→Introductory example: Changed commutative diagram to use svg |
→Definition: Updated diagrams to use svg |
||
Line 28:
with the following property:
:For each [[monomorphism]] ''j'': ''U'' → ''X'' there is a unique morphism ''χ<sub>j</sub>'': ''X'' → Ω such that the following [[commutative diagram]]
[[Image:SubobjectClassifier-02.
:is a [[pullback diagram]]—that is, ''U'' is the [[limit (category theory)|limit]] of the diagram:
[[Image:SubobjectClassifier-03.
The morphism ''χ<sub> j</sub>'' is then called the '''classifying morphism''' for the subobject represented by ''j''.
| |||