Giry代数在概率论中的存在性及其应用
The existence and utility of Giry algebras in probability theory
摘要：
Giry代数是重心映射，它是可收缩余均衡器对的余均衡器（与任何代数一样），它的存在一般要求可测空间被离散两点空间余分离，并假设不存在可测基数.在这一假设下，每一个可测空间，这是余分离有一个代数，和范畴的吉里代数提供了一个方便的设置概率论，因为它是一个对称的monoidal封闭范畴的所有限制和colimits，以及有一个分离子和coseparator。这与吉里单子的克莱西范畴形成鲜明对比，后者经常被用来建模条件概率，它有一个分隔符，但没有太多其他的东西。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
