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A preabelian category is called integral if epimorphisms are stable under pullbacks and monomorphisms are stable under pushouts. A major property of integral category is that by inverting bimorphisms one can turn it into abelian category.

Is it true that the category of abelian varieties over a finite field is integral with bimorphisms being isogenies? If yes, could you give me a relevant reference?

The same question about the category of $p$-divisible groups over a finite field of characteristic $p$ and over the ring of Witt vectors over such a field.

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