This paper describes several cases of adjunction in the homomorphism order of relational structures. For these purposes, we say that two functors $\Gamma$ and $\Delta$ between categories of relational structures are adjoint if for all structures $A$ and $B$, we have that $\Gamma(A)$ maps homomorphically to $B$ if and only if $A$ maps homomorphically to $\Delta(B)$. If this is the case $\Gamma$ is called the left adjoint to $\Delta$ and $\Delta$ the right adjoint to $\Gamma$. In 2015, Foniok and Tardif described some functors 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 relational structures, and coincidentely, 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 motivated by the 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序中的若干伴随情形。为此，我们称关系结构范畴间的两个函子$\Gamma$和$\Delta$是伴随的，当且仅当对所有结构$A$和$B$，$\Gamma(A)$到$B$存在同态映射当且仅当$A$到$\Delta(B)$存在同态映射。此时$\Gamma$称为$\Delta$的左伴随，$\Delta$称为$\Gamma$的右伴随。2015年，Foniok与Tardif描述了有向图范畴中一些兼具左右伴随的函子。他们的主要贡献在于为Pultr于1970年辨识出的某些右伴随函子构造了右伴随。我们将Foniok与Tardif的结果推广至任意关系结构，同时意外地获得了有向图上更多的右伴随；由于这些构造与有限对偶性相关，我们还给出了树对偶的新构造方法。本研究的动机源于承诺约束满足问题的应用——已有研究表明此类函子可作为这些问题间的高效归约手段。