The category of topological spaces is not balanced (since continuous bijections are not necessarily homeomorphisms), while a topos is balanced.
[1] This is one of the reasons why a topos is said to be nicer.
[4] Contrary to what one might expect, a balanced pre-abelian category may not be abelian.
[5] A quasitopos is similar to a topos but may not be balanced.
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