Balanced category

In mathematics, especially in category theory, a balanced category is a category in which every bimorphism is an isomorphism.
The category of topological spaces is not balanced, while a topos is balanced. This is one of the reasons why a topos is said to be nicer.

Examples

The following categories are balanced:

Set, the category of sets.
Grp, the category of groups.
An abelian category.
CHaus, the category of compact Hausdorff spaces.

An additive category may not be balanced. Contrary to what one might expect, a balanced pre-abelian category may not be abelian.
A quasitopos is similar to a topos but may not be balanced.