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:
“It is an inexpressible Pleasure to know a little of the World, and be of no Character or Significancy in it. To be ever unconcerned, and ever looking on new Objects with an endless Curiosity, is a Delight known only to those who are turned for Speculation: Nay, they who enjoy it, must value things only as they are the Objects of Speculation, without drawing any worldly Advantage to themselves from them, but just as they are what contribute to their Amusement, or the Improvement of the Mind.”
—Richard Steele (1672–1729)
“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)