Concrete balanced category A category is called balanced if every bimorphism is an isomorphism.

Consider a concrete category such that every bijective morphism is a isomorphism. Does the category is balanced? Does converse is true?
In the category of rings, every bijective morphism is an isomorphism, but the inclusion of $\mathbb{Z}$ in $\mathbb{Q}$ is a bimorphism that is not an isomorphism, so the category of rings is not balanced.
Generally speaking, whenever you see a definition that says: A thing X is called Y if.....

what they really mean is: A thing X is called Y iff...

In other words the definition is a logical equivalence (a logical biconditional).

The definition of balanced category in ncatlab  is an exanple of this usage