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The answer is yes if $A=R\mbox{-Mod}$ has pullbacks (which I'm pretty sure it does). See Tom Leinster's answeranswer to a similar question.

The answer is yes if $A=R\mbox{-Mod}$ has pullbacks (which I'm pretty sure it does). See Tom Leinster's answer to a similar question.

The answer is yes if $A=R\mbox{-Mod}$ has pullbacks (which I'm pretty sure it does). See Tom Leinster's answer to a similar question.

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Finn Lawler
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The answer is yes if $A=R\mbox{-Mod}$ has pullbacks (which I'm pretty sure it does). See Tom Leinster's answer to a similar question.