In this paper we investigate algebraic properties of big Ramsey degrees in categories satisfying some mild conditions. As the first nontrivial consequence of the generalization we advocate in this paper we prove that small Ramsey degrees are the minima of the corresponding big ones. We also prove that big Ramsey degrees are subadditive and show that equality is enforced by an abstract property of objects we refer to as self-similarity. Finally, we apply the abstract machinery developed in the paper to show that if a countable relational structure has finite big Ramsey degrees, then so do its quantifier-free reducts. In particular, it follows that the reducts of $(\mathbb{Q},<)$, the random graph, the random tournament and $(\mathbb{Q},<,0)$ all have finite big Ramsey degrees.

在本文中，我们研究了满足某些温和条件的类别中的大拉姆齐度的代数性质。作为本文推广的第一个非平凡结果，我们证明了较小的Ramsey度是相应的较大的Ramsey度的极小值。我们还证明了大的拉姆西度数是次加性的，并且表明相等性是由我们称为自相似性的对象的抽象属性强制实施的。最后，我们使用本文中开发的抽象机制来表明，如果可数关系结构具有有限的大拉姆西度，那么其无量词的还原也是如此。特别地，由此得出$（\mathbb{问}，<）$，随机图，随机锦标赛和 $（\mathbb{问}，<，0）$ 都具有有限的大拉姆齐度。