On a category of cluster algebras

Details On a category of cluster algebras On a category of cluster algebras

2012-01-28

arxiv.org/abs/1201.5986v1

Mathematics

Representation Theory

37 pages

Scientific paper

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.

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