We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial...We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial＂ edition of preseed mutations. Every Weyl preseed p gives rise to a categorical preseed P which generates a clustered hyperbolic category; this is formed by copies of categories each one of which is equivalent to the category of representations of the Weyl cluster algebra H（p）. A ＂categorical realization＂ of Weyl cluster algebra is provided in the sense of defining a map Fp from any clustered hyperbolic category induced from p to the Weyl cluster algebra H（p）, where the image of Fp generates H（p）.展开更多
文摘We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial＂ edition of preseed mutations. Every Weyl preseed p gives rise to a categorical preseed P which generates a clustered hyperbolic category; this is formed by copies of categories each one of which is equivalent to the category of representations of the Weyl cluster algebra H（p）. A ＂categorical realization＂ of Weyl cluster algebra is provided in the sense of defining a map Fp from any clustered hyperbolic category induced from p to the Weyl cluster algebra H（p）, where the image of Fp generates H（p）.
