群范畴

Abel群范畴是一个Abel范畴，在这个范畴中，两个子对象的交就是两个子群的交，两个子对象的并是由两个子群的并生成的子群。

Abel group category is an abel category . In this category , the intersection of two subobjects is the intersection of two subgroups and the union of two subjects is the subgroup generated by the union of two subgroups .

群范畴中的自由对象及其生成元集

A free object and its generators set in group category

将Abel范畴所得的正合关系式应用于Abel群范畴中，就得到一些关于子群的交、并和直和之间的群的同构关系式，在交换群中推广了群的同构定理。

The exact sequences we get in Abel category induce some isomorphism relations of Abel groups .

设H为有限Hopf代数，B为交换环，H0为交换、余交换的有限Hopf代数范畴，C为交换环范畴，A为交换群范畴。

Let H be a finite Hopf algebra , B a commutative ring , H 0 the category of all commutative , co-commutative finite algebra , C the category of commutative rings and A of commutative groups .

并说明在有限生成的阿贝尔群范畴内F-同构是一等价关系，否则不然。

We also consider the Five Lemma in the case of F-isomorphism and F & exactness , It is shown that in the category of finitely generated abelian groups the F-isomorphism is an equivalent relation but is not true out of this category .

为此本论文首先界定城市群概念、范畴及进行相关研究综述，再分析世界城市化发展态势及对国内城市群进行比较研究，从而在更广阔的视角上分析成渝城市群。

This paper defined concepts , scope and associated research , and then analyzed world development trend of urbanization and comparative study of domestic .

本文将经典的对称群和模糊对称群溶为一体，提出一种新的代数结构&CF对称群范畴，并从范畴论的角度出发，给出了对系统进行统一描述的方法。

With classical symmetric group and fuzzy symmetric group of mix together for integral whole , this paper set out a new algebra construction-the CF the category of symmetric group , and from the category give classic out method towards system proceed unify describe .

据此，本文试探性地提出了水词群的认知模型，并考虑到文化模型对认知模型的影响，对水词群的范畴化过程进行总结。

Based on this , the thesis tentatively puts forward a cognitive model of WATER , considering the influence of cultural model .