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:
“Words express neither objects nor ourselves.”
—Johann Wolfgang Von Goethe (1749–1832)
“All objects look well through an arch.”
—Herman Melville (1819–1891)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)