Category Theory and Living Systems

1. The problem. The phenomenology of living systems (i.e., their relation to the physical world) does not yet have a satisfactory theory. This is not just a philosophical issue. In order to emulate the skill and subtlety of biological computation in our own machines and systems, we need to understand what are the means by which such veridicality is obtained. Any person is capable of amazing feats of computational accuracy for which current biological accounts are completely inadequate. To awake at a set hour without external clues, to catch a ball hit to some distant point in space (running on deadreckoning to the exact spot), to execute complex choreography ending exactly with the music (even when that music has only been heard a few times), to measure out in a glance exactly one kilo of coffee beans, these aspects of exquisite control seem to require explanation that is principled and coherent. I believe that mathematical principles play a role in all biological computation, and that a formal categorical substrate underlies the messy ad hoc networks of living systems. Whether or not such a platonic (or really Leibnizian) view is found to hold in nature, it could be helpful for our emulations. In the remainder of this paper, we sketch some arguments and history for the use of categories in biology in section 2. The origin of weak adjointness (in algebraic topology) is discussed in section 3, while in section 4, the precise definition is given. Finally, the last section considers applications to our basic problem.