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:
“Nobody seriously questions the principle that it is the function of mass culture to maintain public morale, and certainly nobody in the mass audience objects to having his morale maintained.”
—Robert Warshow (1917–1955)
“Women have seldom sufficient employment to silence their feelings; a round of little cares, or vain pursuits frittering away all strength of mind and organs, they become naturally only objects of sense.”
—Mary Wollstonecraft (1759–1797)
“I do not know that I meet, in any of my Walks, Objects which move both my Spleen and Laughter so effectually, as those Young Fellows ... who rise early for no other Purpose but to publish their Laziness.”
—Richard Steele (1672–1729)