The trivial ring, among all unital rings, has two characteristic properties:
there is a unique function into the trivial ring, from any other unital ring;
there is no function from the trivial ring, except to itself.
The first property generalizes to arbitrary categories as the property of a terminal object.
The corresponding generalization including also the second property is that of a strict terminal object:
A terminal object is called a strict terminal object if every morphism from is an isomorphism:
In other words, a strict terminal object is a maximal terminal object.
Trivial unital ring
Trivial Boolean algebra
Trivial absorption monoid
In general, for any algebraic theory with two constants and and a binary operation for which is a (left) absorbing element and is a (left) unit, the trivial model is strictly terminal.
Last revised on March 17, 2023 at 15:01:08. See the history of this page for a list of all contributions to it.