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
Famous quotes containing the word definition:
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)