Natural organized systems adapt to internal and external pressures and this happens at all levels of the abstraction hierarchy. Wanting to think clearly about this idea motivates our paper, and so the idea is elaborated extensively in the introduction, which should be broadly accessible to a philosophically-interested audience. In the remaining sections, we turn to more compressed category theory. We define the monoidal double category Org of dynamic organizations, we provide definitions of Org-enriched, or dynamic, categorical structures -- e.g. dynamic categories, operads, and monoidal categories -- and we show how they instantiate the motivating philosophical ideas. We give two examples of dynamic categorical structures: prediction markets as a dynamic operad and deep learning as a dynamic monoidal category.

翻译：自然组织的系统会适应内部和外部的压力，这种适应发生在抽象层级的所有层面。清晰思考这一概念的愿望促成了本文的撰写，因此该观点在引言部分得到详尽阐述，并对具有哲学兴趣的读者具有广泛的可理解性。在后续章节中，我们转向更简洁的范畴论。我们定义了动态组织的幺半双重范畴Org，提供了Org-enriched（即动态）范畴结构的定义——例如动态范畴、操作代数和幺半范畴——并展示了它们如何具体体现催生本文的哲学思想。我们给出了两个动态范畴结构的实例：作为动态操作代数的预测市场和作为动态幺半范畴的深度学习。