Zero Element - Zero Objects

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)