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:
“Little minds mistake little objects for great ones, and lavish away upon the former that time and attention which only the latter deserve. To such mistakes we owe the numerous and frivolous tribe of insect-mongers, shell-mongers, and pursuers and driers of butterflies, etc. The strong mind distinguishes, not only between the useful and the useless, but likewise between the useful and the curious.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“But what is classification but the perceiving that these objects are not chaotic, and are not foreign, but have a law which is also the law of the human mind?”
—Ralph Waldo Emerson (1803–1882)