AI 中文总结
研究代数乘法序列间余代数测度及其在霍赫希尔德同调上诱导映射，借助洗牌积构建相关理论，发展通用测度余代数，通过双模理论研究余模测度诱导映射及丰富范畴，还考虑余乘法序列诱导的测度等。
AI 中文摘要
我们研究代数乘法序列之间的余代数测度以及它们在霍赫希尔德同调上诱导的映射。乘法序列的霍赫希尔德理论被引入为一个在链复形的对称幺半范畴中取值于分次代数的函子，借助洗牌积构建。我们发展了通用测度余代数，即乘法序列的斯威德勒同调，还研究了此背景下的其他几种斯威德勒运算。特别地，我们得到了乘法序列在余交换余代数上的丰富化。利用乘法序列上适当的双模理论，我们研究余模测度在带系数的霍赫希尔德理论上诱导的映射以及相应的丰富范畴。最后，我们考虑由余代数的余乘法序列诱导的乘法序列之间的测度和广义斯威德勒运算，以及从中得到的霍赫希尔德理论中的映射。
英文摘要
We study coalgebra measurings between multiplicative sequences of algebras and the maps induced by them on Hochschild homology. The Hochschild theory of multiplicative sequences is introduced as a functor taking values in graded algebras in the symmetric monoidal category of chain complexes, constructed with the help of the shuffle product. We develop the universal measuring coalgebra, or Sweedler Hom for multiplicative sequences, as well as study several other Sweedler operations in this context. In particular, we obtain an enrichment of multiplicative sequences over cocommutative coalgebras. Using an appropriate theory of bimodules over multiplicative sequences, we study maps induced by comodule measurings on the Hochschild theory with coefficients, as well as the corresponding enriched categories. Finally, we consider measurings and generalized Sweedler operations between multiplicative sequences induced by comultiplicative sequences of coalgebras, and also the maps in Hochschild theory obtained from them.
