← 研踪 PaperTrailarXiv:2611.02142 · v1
Homomorphisms on a product of free convex semilattices
首次提交 2026-11-02 03:21
版本更新 2026-11-02 03:21
雷达观测 2026-11-04 23:43
摘要
Convex semilattices form an equational class that combines convex algebras and semilattices by a distributive law. For a set $I$ let $\mathcal FI$ be the free convex semilattice with basis $I$. A product $\mathcal FI\times\mathcal FJ$ is generated by $I\times J$, but is not free. Hence, not every map from $I\times J$ into an arbitrary convex semilattice $X$ extends uniquely to a homomorphism from $\mathcal FI\times\mathcal FJ$ to $X$. We investigate a condition on a map $\varphi$ of $I\times J$ into some convex semilattice $X$ that is always necessary and often sufficient for $\varphi$ to have such an extension to a homomorphism $Φ$ of $\mathcal FI\times\mathcal FJ$ into $X$.
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-02 03:21 · 最新观测版本
Homomorphisms on a product of free convex semilattices
Convex semilattices form an equational class that combines convex algebras and semilattices by a distributive law. For a set $I$ let $\mathcal FI$ be the free convex semilattice with basis $I$. A product $\mathcal FI\times\mathcal FJ$ is generated by $I\times J$, but is not free. Hence, not every map from $I\times J$ into an arbitrary convex semilattice $X$ extends uniquely to a homomorphism from $\mathcal FI\times\mathcal FJ$ to $X$. We investigate a condition on a map $\varphi$ of $I\times J$ into some convex semilattice $X$ that is always necessary and often sufficient for $\varphi$ to have such an extension to a homomorphism $Φ$ of $\mathcal FI\times\mathcal FJ$ into $X$.
查看此版本解读 →查看此版本原文 ↗