论文标题
概率理论中的Giry代数的存在和实用性
The existence and utility of Giry algebras in probability theory
论文作者
论文摘要
Giry代数是Barycenters图，它们是可缩度的均衡器对（如任何代数）的均衡器，并且它们的存在通常需要通过离散的两个点空间来促进可衡量的空间，并且假设不存在可测量的Cardinal的假设。在这一假设下，每个可培养的可衡量空间都有一个代数，而Giry代数类别为概率理论提供了方便的设置，因为它是具有所有限制和colimits的对称单体封闭类别，并且具有Seperator和coseperator和coseperator。这与Giry Monad的Kleisi类别形成了鲜明的对比，Giry Monad通常用于建模有条件的概率，该概率具有Semperator，但并不是其他。
Giry algebras are barycenters maps, which are coequalizers of contractible coequalizer pairs (like any algebras), and their existence, in general, requires the measurable space be coseparated by the discrete two point space, and the hypothesis that no measurable cardinals exist. Under that hypothesis, every measurable space which is coseparated has an algebra, and the category of Giry algebras provides a convenient setting for probability theory because it is a symmetric monoidal closed category with all limits and colimits, as well as having a seperator and coseperator. This is in stark contrast to the Kleisi category of the Giry monad, which is often used to model conditional probability, which has a seperator but not much else.
