So in Weibel, he states

Warning: In an unbounded spectral sequence, we will tacitly assume that $B^{\infty}$, $Z^{\infty}$, and $E^{\infty}$ exist! The reader who is willing to only work in the category of modules may ignore this difficulty. The queasy reader should assume that the abelian category A satisfies axioms {AB4) and (AB4*).

But, I don't understand the requirement of AB4* at all. I know AB3 and AB3* are needed for sure for the limits and colimits and I believe that with AB5, we can get that they are all subobjects with the correct containment relations. Then, why does Weibel insist on AB4*?


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