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For questions on limits and colimts in the sense of category theory, and related notions.

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Does a fully faithful functor always preserve limits and colimits?

The forgetful functor from abelian groups to groups is fully faithful, and does not preserve coproducts. For example, in abelian groups, $\mathbb Z\coprod \mathbb Z=\mathbb Z\times \mathbb Z$, but in …
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