Is it true that an additive functor between abelian categories commutes with colimits if it's right-exact and commutes with (arbitrary) direct sums?
If yes, does someone know a good source of a proof?
2026-04-02 21:47:00.1775166420
When does a functor commute with colimits?
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In a category with coproducts and coequalizers, any colimit can be built out of coproducts and coequalizers. This is a nice exercise. In an $\text{Ab}$-enriched category, coequalizers can be replaced with cokernels. This is another nice exercise.