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: Zero Element
Famous quotes containing the word objects:
“in the mind of man,
A motion and a spirit, that impels
All thinking things, all objects of all thought,
And rolls through all things.”
—William Wordsworth (1770–1850)
“We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
—Selma H. Fraiberg (20th century)