Algebraic K0 for unpointed categories

IF 0.5 3区 数学 Q3 MATHEMATICS
Felix Küng
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引用次数: 0

Abstract

We construct a natural generalization of the Grothendieck group K0 to the case of possibly unpointed categories admitting pushouts by using the concept of heaps recently introduced by Brezinzki. In case of a monoidal category, the defined K0 is shown to be a truss. It is shown that the construction generalizes the classical K0 of an abelian category as the group retract along the isomorphism class of the zero object. We finish by applying this construction to construct the integers with addition and multiplication as the decategorification of finite sets and show that in this K0(Top̲) one can identify a CW-complex with the iterated product of its cells.

无指向类别的代数 K0
我们利用布雷津斯基(Brezinzki)最近提出的 "堆"(heaps)概念,构建了格罗内迪克群(Grothendieck group K0)的自然广义,使其适用于可能无指向的、允许推出的范畴。在一元范畴的情况下,定义的 K0 被证明是一个桁。结果表明,随着群沿着零对象的同构类缩回,这种构造概括了经典的无性类 K0。最后,我们将这一构造应用于构建整数的加法和乘法,作为有限集的解归类,并证明在这个 K0(Top̲) 中,我们可以将一个 CW 复数与它的单元的迭积相鉴别。
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来源期刊
CiteScore
1.50
自引率
12.50%
发文量
226
审稿时长
4-8 weeks
期刊介绍: The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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