论文标题
Grothendieck类别和相对HOPF对象中的综合理论
Comodule theories in Grothendieck categories and relative Hopf objects
论文作者
论文摘要
我们通过Grothendieck类别$ \ Mathfrak s $开发了comodule类别的非交通基本变化的分类代数。我们描述了所产生的综合类别何时在本地有限生成，本地noetherian或可以作为模块类别的非共同基础变化的核心反射子类别恢复。我们还介绍了相对$（a，h）$ - $ \ mathfrak s $的类别$ {_ a} \ mathfrak s^h $，其中$ h $是hopf代数，$ a $ a $是正确的$ h $ comcomodule -odule代数。我们通过频谱序列研究了$ {_ a} \ mathfrak s^h $中的共同体理论。使用共同引导函数和共同变量的函子，我们研究扭转理论及其与$ {_ a} \ Mathfrak S^H $中的注射分辨率之间的关系。最后，我们使用模块类别的非共同基础变化中相关的素数和支持理论，以$ {_ a} \ Mathfrak s^H $中的最小内注射分辨率的直接总和分解。
We develop the categorical algebra of the noncommutative base change of a comodule category by means of a Grothendieck category $\mathfrak S$. We describe when the resulting category of comodules is locally finitely generated, locally noetherian or may be recovered as a coreflective subcategory of the noncommutative base change of a module category. We also introduce the category ${_A}\mathfrak S^H$ of relative $(A,H)$-Hopf modules in $\mathfrak S$, where $H$ is a Hopf algebra and $A$ is a right $H$-comodule algebra. We study the cohomological theory in ${_A}\mathfrak S^H$ by means of spectral sequences. Using coinduction functors and functors of coinvariants, we study torsion theories and how they relate to injective resolutions in ${_A}\mathfrak S^H$. Finally, we use the theory of associated primes and support in noncommutative base change of module categories to give direct sum decompositions of minimal injective resolutions in ${_A}\mathfrak S^H$.
