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 χ j: X → Ω such that the following commutative diagram
- is a pullback diagram — that is, U is the limit of the diagram:
The morphism χ j is then called the classifying morphism for the subobject represented by j.
Read more about this topic: Subobject Classifier
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