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:
“I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way. But in this water there are countless objects at different depths; and certain influences will give certain kinds of those objects an upward influence which may be intense enough and continue long enough to bring them into the upper visible layer. After the impulse ceases they commence to sink downwards.”
—Charles Sanders Peirce (1839–1914)
“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)