We explain why every non‐trivial exact tensor functor on the triangulated category of mixed motives over a field $\mathbb{F}$ has zero kernel, if one assumes ‘all’ motivic conjectures. In other words, every non‐zero motive generates the whole category up to the tensor triangulated structure. Under the same assumptions, we also give a complete classification of triangulated étale motives over $\mathbb{F}$ with integral coefficients, up to the tensor triangulated structure, in terms of the characteristic and the orderings of $\mathbb{F}$.

中文翻译：

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关于坦纳克语类别和混合动机的注释

我们解释了为什么在一个场上混合动机的三角分类上的每个非平凡精确张量函子 $\mathbb{F}$如果假设“所有”动机猜想，则内核为零。换句话说，每个非零动机都会生成整个类，直到张量三角结构。在相同的假设下，我们还对三角情节动机进行了完整的分类$\mathbb{F}$ 就特征和阶而言，具有积分系数，直至张量三角结构 $\mathbb{F}$。