In semi-abelian varieties of algebras, all Yoneda n-step extension collections between fixed objects admit a set of representatives, so cohomology objects are small.
Bourn,Normalization equivalence, kernel equivalence and affine categories, Category The- ory, Proceedings Como 1990 (A
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The cohomology objects of a semi-abelian variety are small
In semi-abelian varieties of algebras, all Yoneda n-step extension collections between fixed objects admit a set of representatives, so cohomology objects are small.