迹积与伪积：带投影的限制类半群
Trace- and pseudo-products: restriction-like semigroups with a band of projections
摘要：
我们确定了范畴和半群上允许分别构造伪积和迹积的条件和结构，使它们之间的联系尽可能精确。本课题以ESN定理及其在充分半群上的推广为模型。与ESN的其他变体不同，它是自对偶的（双边的），并且交换投影的条件被放松。投影形成带（在乘法下闭合）的条件被证明是非常自然的。单侧约被认为是，并比较（广义）D-半群。最后考察了范畴是广群时的特殊情形。
英文摘要：
We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem and its generalization to ample semigroups. Unlike some other variants of ESN, it is self-dual (two-sided), and the condition of commuting projections is relaxed. The condition that projections form a band (are closed under multiplication) is shown to be a very natural one. One-sided reducts are considered, and compared to (generalized) D-semigroups. Finally the special case when the category is a groupoid is examined.
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。
