trivial algebra

Every algebraic category (in just about any sense of the term) has a terminal object which is usually called the **trivial algebra**, often denoted $0$ or $1$. Its underlying set is a singleton, and every algebraic operation $1^n \to 1$ is the unique function to the singleton set.

- The singleton set is itself the trivial set.
- The trivial group is the trivial group.
- The trivial ring is the trivial ring.
- The $0$-dimensional vector space is the trivial vector space.
- The trivial Lie algebra is the trivial Lie algebra.
- The trivial category is the trivial strict category.

Created on September 4, 2010 19:16:36
by Toby Bartels
(173.190.156.19)