Characterizing consciousness in and of itself is notoriously difficult. Here, we propose an alternative approach to characterize, and eventually define, consciousness through exhaustive descriptions of consciousness’ relationships to all other consciousness. This approach is founded in category theory. Indeed, category theory can prove that two objects A and B in a category can be equivalent if and only if all the relationships that A holds with others in the category are the same as those of B; this proof is called the Yoneda lemma. To introduce the Yoneda lemma, we gradually introduce key concepts of category theory to consciousness researchers. Along the way, we propose several possible definitions of categories of consciousness, both in terms of level and contents, through the usage of simple examples. We propose to use the categorical structure of consciousness as a gold standard to formalize empirical research (e.g. color qualia structure at fovea and periphery) and, especially, the empirical testing of theories of consciousness.

中文翻译：

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意识的关系方法：意识的层次和内容的类别

描述意识本身是出了名的困难。在这里，我们提出了一种替代方法，通过对意识与所有其他意识的关系进行详尽的描述来表征并最终定义意识。这种方法是建立在范畴论的基础上的。事实上，范畴论可以证明一个范畴中的两个对象A和B可以等价，当且仅当A与范畴中其他对象的所有关系都与B相同时；这个证明被称为米田引理。为了介绍米田引理，我们逐渐向意识研究者介绍范畴论的关键概念。在此过程中，我们通过使用简单的例子，在层次和内容方面提出了意识类别的几种可能的定义。我们建议使用意识的分类结构作为黄金标准来形式化实证研究（例如中央凹和外围的颜色感受质结构），特别是意识理论的实证检验。