论文标题
抗道和三角引理
Anticommutativity and the triangular lemma
论文作者
论文摘要
对于多种$ \ Mathcal {v} $，最近已经显示，二进制产品在当地的任意同时化器中通勤，即，在点的每一个纤维中，$π：\ Mathrm {pt}（pt}（\ Mathbb {c}）（c}） $ \ MATHCAL {V} $。在本文中，我们建立了一个类似的结果，该结果将通用代数中所谓的三角形引理与某个类别$ \ textit {antymutativity} $条件连接起来。特别是，我们表明这种反交换性及其本地版本是Mal'TSEV条件，本地版本等于回调上的三角形引理。作为推论，每个本地抗议品种$ \ mathcal {v} $在DUDA的意义上都有直接可分配的一致性课程，并且如果$ \ Mathcal {v} $是同性的，则相反的是。
For a variety $\mathcal{V}$, it has been recently shown that binary products commute with arbitrary coequalizers locally, i.e., in every fibre of the fibration of points $π: \mathrm{Pt} (\mathbb{C}) \rightarrow \mathbb{C}$, if and only if Gumm's shifting lemma holds on pullbacks in $\mathcal{V}$. In this paper, we establish a similar result connecting the so-called triangular lemma in universal algebra with a certain categorical $\textit{anticommutativity}$ condition. In particular, we show that this anticommutativity and its local version are Mal'tsev conditions, the local version being equivalent to the triangular lemma on pullbacks. As a corollary, every locally anticommutative variety $\mathcal{V}$ has directly decomposable congruence classes in the sense of Duda, and the converse holds if $\mathcal{V}$ is idempotent.
