I equip the category of presheaves $[\mathcal{D}^{op},\text{Gpd}]$ with the injective model structure ($\mathcal{D}$ is just any small category). In this structure, weak equivalences and cofibrations are componentwise. One can notice that fibrations are in particular componentwise fibrations (but the converse is not true). Are there sufficient conditions on a componentwise fibration to be a (injective) fibration ?
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