This paper describes several cases of adjunction in the homomorphism preorder of relational structures. We say that two functors $\Lambda$ and $\Gamma$ between thin categories of relational structures are adjoint if for all structures $\mathbf A$ and $\mathbf B$, we have that $\Lambda(\mathbf A)$ maps homomorphically to $\mathbf B$ if and only if $\mathbf A$ maps homomorphically to $\Gamma(\mathbf B)$. If this is the case, $\Lambda$ is called the left adjoint to $\Gamma$ and $\Gamma$ the right adjoint to $\Lambda$. In 2015, Foniok and Tardif described some functors on the category of digraphs that allow both left and right adjoints. The main contribution of Foniok and Tardif is a construction of right adjoints to some of the functors identified as right adjoints by Pultr in 1970. We generalise results of Foniok and Tardif to arbitrary relational structures, and coincidently, we also provide more right adjoints on digraphs, and since these constructions are connected to finite duality, we also provide a new construction of duals to trees. Our results are inspired by an application in promise constraint satisfaction -- it has been shown that such functors can be used as efficient reductions between these problems.

翻译：本文描述了关系结构同态预序中的若干伴随情形。我们称关系结构薄范畴中的两个函子$\Lambda$与$\Gamma$构成伴随对，当且仅当对于任意结构$\mathbf A$与$\mathbf B$，$\Lambda(\mathbf A)$可同态映射至$\mathbf B$等价于$\mathbf A$可同态映射至$\Gamma(\mathbf B)$。此时$\Lambda$称为$\Gamma$的左伴随，$\Gamma$称为$\Lambda$的右伴随。2015年，Foniok与Tardif描述了有向图范畴中若干兼具左右伴随的函子，其核心贡献在于为Pultr于1970年确定的某些右伴随函子构造了相应的右伴随。本文将Foniok与Tardif的结论推广至任意关系结构，同时偶然地给出了有向图上更多右伴随的构造。由于这些构造与有限对偶性相关联，我们还提供了树结构对偶的一种新构造方法。本研究受承诺约束满足问题中应用需求的启发——已有研究表明此类函子可作为该问题间的高效归约工具。