论文标题
各向同性和组合问题
Isotropy and Combination Problems
论文作者
论文摘要
在上一篇论文中，作者及其合作者在单分级方程理论的背景下研究了各向同性现象，并表明任何此类理论的模型类别的各向同性群体都编码了该理论内部自动形态的概念。 利用术语重写理论中组合问题的结果，我们在本文中表明，如果$ \ mathbb {t} _1 $和$ \ mathbb {t} _2 $是（脱节）方程理论满足最小假设，那么任何无限期的，有限的，有限的，有限地生成的模型的联盟理论的模型\ mathbb {t} _2 $具有微不足道的各向同性组，因此，此类模型的唯一内部自动形态，即此类模型的唯一相干扩展的自动形态，是身份自动形态。 作为推论，我们表明模型类别的全局各向同性组$（\ Mathbb {t} _1 + \ Mathbb {t} _2 _2）\ Mathsf {modsf {modsf {modsf {mod} $，即该类别中心的可逆元素组。
In a previous paper, the author and his collaborators studied the phenomenon of isotropy in the context of single-sorted equational theories, and showed that the isotropy group of the category of models of any such theory encodes a notion of inner automorphism for the theory. Using results from the treatment of combination problems in term rewriting theory, we show in this article that if $\mathbb{T}_1$ and $\mathbb{T}_2$ are (disjoint) equational theories satisfying minimal assumptions, then any free, finitely generated model of the disjoint union theory $\mathbb{T}_1 + \mathbb{T}_2$ has trivial isotropy group, and hence the only inner automorphisms of such models, i.e. the only automorphisms of such models that are coherently extendible, are the identity automorphisms. As a corollary, we show that the global isotropy group of the category of models $(\mathbb{T}_1 + \mathbb{T}_2)\mathsf{mod}$, i.e. the group of invertible elements of the centre of this category, is the trivial group.
