On a category of cluster algebras
On a category of cluster algebras
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DOI：
10.1016/j.jpaa.2013.07.005
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发表时间：
2012-01
影响因子：
0.8
通讯作者：
I. Assem;G. Dupont;R. Schiffler
中科院分区：
文献类型：
--
作者：
I. Assem;G. Dupont;R. Schiffler
引入一类具有固定初始种子的簇代数。这个范畴有可数的上积，可以组合构造，但没有积。我们讨论了这一范畴中的同构和单态，并给出了构造特殊的单态和满态类的组合方法。在簇代数的情况下，从表面，我们描述了这一类和几何形状的表面之间的相互作用。
We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characterise isomorphisms and monomorphisms in this category and provide combinatorial methods for constructing special classes of monomorphisms and epimorphisms. In the case of cluster algebras from surfaces, we describe interactions between this category and the geometry of the surfaces.