再论标准三角剖分的标准性
Revisiting the canonicity of canonical triangulations
摘要：
稳定的导子提供了一个增强的三角范畴，是由存在的典型三角。本文证明了稳定导子的正合态射诱导出标准三角剖分的正合函子，对于任意自然变换也是如此。这个2-范畴加细也提供了关于典范三角剖分的唯一性陈述。这些结果依赖于一个更仔细的研究态射的导子和这项研究是独立的兴趣。我们分析了导子的态射与极限、余极限和Kan扩展之间的相互作用，包括讨论了Kan扩展类由固定态射保持的不变性和封闭性。
英文摘要：
Stable derivators provide an enhancement of triangulated categories as is indicated by the existence of canonical triangulations. In this paper we show that exact morphisms of stable derivators induce exact functors of canonical triangulations, and similarly for arbitrary natural transformations. This 2-categorical refinement also provides a uniqueness statement concerning canonical triangulations. These results rely on a more careful study of morphisms of derivators and this study is of independent interest. We analyze the interaction of morphisms of derivators with limits, colimits, and Kan extensions, including a discussion of invariance and closure properties of the class of Kan extensions preserved by a fixed morphism.
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