Suppose in an Abelian category $\mathscr C$, the direct sum of any family of objects exists, then is $\bigoplus_{i\in\varnothing}A_i$ equal to 0 or meaningless?
2026-03-29 16:50:08.1774803008
The direct sum of any family of objects
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An empty direct sum in an abelian category is a zero object.
In general:
An empty product is a terminal object (provided that the category has terminal objects).
An empty coproduct is an initial object (provided that the category has initial objects).