Transport of structure in higher homological algebra
Transport of structure in higher homological algebra
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DOI：
10.1016/j.jalgebra.2021.01.019
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发表时间：
2020-03
影响因子：
0.9
通讯作者：
Raphael Bennett-Tennenhaus;Amit Shah
中科院分区：
文献类型：
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作者：
Raphael Bennett-Tennenhaus;Amit Shah
我们填补了文献中的空白，关于“运输结构”的（n+ 2）-角度，n-精确，n-阿贝尔和n-exangulated类别出现在（古典和高等）同调代数。作为我们的主要结果的应用，我们表明，这些种类的范畴之一的骨架继承了相同的结构，在一个典型的方式，等价。特别地，由此得出弱（n+ 2）-角化范畴的骨架实际上是我们所称的强（n+ 2）-角化范畴。当n= 1时，这澄清了与集群类别的定义有关的技术问题。我们还介绍了一个n-exangulated函子之间的n-exangulated范畴的概念。当范畴是（n + 2）-角化的时，这恢复了（n+ 2）-角化函子的定义;当范畴是n-正合的时，这恢复了正合函子的更高类似。
We fill a gap in the literature regarding ‘transport of structure’for (n+ 2)-angulated, n-exact, n-abelian and n-exangulated categories appearing in (classical and higher) homological algebra. As an application of our main results, we show that a skeleton of one of these kinds of categories inherits the same structure in a canonical way, up to equivalence. In particular, it follows that a skeleton of a weak (n+ 2)-angulated category is in fact what we call a strong (n+ 2)-angulated category. When n= 1 this clarifies a technical concern with the definition of a cluster category. We also introduce the notion of an n-exangulated functor between n-exangulated categories. This recovers the definition of an (n+ 2)-angulated functor when the categories concerned are (n+ 2)-angulated, and the higher analogue of an exact functor when the categories concerned are n-exact.