Zero Objects
A zero object in a category is both an initial and terminal object (and so an identity under both coproducts and products). For example, the trivial structure (containing only the identity) is a zero object in categories where morphisms must map identities to identities. Specific examples include:
- The trivial group, containing only the identity (a zero object in the category of groups)
- The zero module, containing only the identity (a zero object in the category of modules over a ring)
Read more about this topic: List Of Zero Terms
Famous quotes containing the word objects:
“The cart before the horse is neither beautiful nor useful. Before we can adorn our houses with beautiful objects the walls must be stripped, and our lives must be stripped, and beautiful housekeeping and beautiful living laid for a foundation.”
—Henry David Thoreau (1817–1862)
“Consciousness, we shall find, is reducible to relations between objects, and objects we shall find to be reducible to relations between different states of consciousness; and neither point of view is more nearly ultimate than the other.”
—T.S. (Thomas Stearns)