Is the category of $\mathbb{Z}$-graded modules over a graded-commutative ring an AB5 category? It is abelian, the subobjects of each object form a set, and it admits arbitrary coproducts. But I don't quite see how the 'filtered colimits of exact sequences are exact part' works.
2026-03-26 11:47:52.1774525672
Is the category of graded modules over a graded-commutative ring an AB5 category?
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