  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.
