We say a category is trivial if any object is a zero object. Suppose the conditions are satisfied. It follows that any object is unitary. Suppose X is an object in a category with a terminate 0 . An arrow with domain X is monomorphic if and only if its codomain is non-terminal.
Any simple object is unitary.
Suppose f is an arrow having a kernel pair. The dual notion of a regular epimorphism is a regular monomorphism . Suppose X is an object in a category with a strict terminate 0 . Y is any arrow. Since 0 is strict, Z must be terminate.