Does the definition of a monoidal abelian category require any coherence between the abelian structure and the monoidal structure?
Definition of a *Monoidal Abelian Category*
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category-theory
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1Obviously the answer is that depends one what you're using the notion of *monoidal abelian category* for. But I'd think that the condition Zhen Lin mentions is a very reasonable one. – 2012-08-01
1 Answers
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At a minimum, you should require that the monoidal structure is additive in each variable, as Zhen Lin says in the comments.