Objects
An object A in a category is said to be:
- isomorphic to an object B provided that there is an isomorphism between A and B.
- initial provided that there is exactly one morphism from A to each object B; e.g., empty set in Set.
- terminal provided that there is exactly one morphism from each object B to A; e.g., singletons in Set.
- a zero object if it is both initial and terminal, such as a trivial group in Grp.
An object A in an abelian category is:
- simple if it is not isomorphic to the zero object and any subobject of A is isomorphic to zero or to A.
- finite length if it has a composition series. The maximum number of proper subobjects in any such composition series is called the length of A.
Read more about this topic: Glossary Of Category Theory
Famous quotes containing the word objects:
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—Ralph Waldo Emerson (1803–1882)
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—Selma H. Fraiberg (20th century)
“By degrees we may come to know the primitive sense of the permanent objects of nature, so that the world shall be to us an open book, and every form significant of its hidden life and final cause.”
—Ralph Waldo Emerson (1803–1882)