# Regarding condition $AB5$

My question is regarding the condition $$AB5$$ for an abelian category $$\mathcal{A}$$ i.e. direct sums exists and filtered colimits are exact. Now taking colimit is right exact in an abelian category given the colimit exists. Say I'm given monomorphisms $$\phi_{i}: M_{i} \rightarrow N_{i}$$ indexed over filtered category $$I$$. The kernel is a finite limit. Now, I know filtered colimit commutes with finite limit when the target category is $$Sets$$. Then does it mean when the target category is an arbitrary abelian category, then filtered colimit need not commute with kernel? More generally, I would like to have some idea on what kind of target category does this commutativity hold?

(In a sense, this occurs in nature quite often, i.e. take $$\mathcal{A}=(\mathrm{Mod-}R)^{op}$$. Then this is typically not an AB5-category since inverse limits are typically not exact in $$\mathrm{Mod-}R$$.)