A NOTE ON THE ABELIANIZATION FUNCTOR

作者：Bourn Dominique; Janelidze Zurab^*

来源：Communications in Algebra, 2016, 44(5): 2009-2033.

DOI：10.1080/00927872.2014.982808

• Abelian category
• Abelian object
• Abelianization
• Approximate subtraction
• Internal abelian group
• Internal subtraction
• Subtractive category
• Subtractive variety

It is well known that the abelianization of a group G can be computed as the cokernel of the diagonal morphism (1(G),1(G)) : G -> G x G in the category of groups. We generalize this to arbitrary regular subtractive categories, among which are the category of groups, the category of topological groups, and the categories of other group-like structures. We also establish that an abelian category is the same as a regular subtractive category in which every monomorphism is a kernel of some morphism.

• 出版日期2016