This is a good question without an obvious answer.

An almost mathematical approach to answering this question is the whimsical proposal of a category Reality introduced in

R.E. Lauro, Beyond the colonization of human imagining and everyday life: Crafting mythopoeic lifeworlds as a theological response to hyperreality, Ph.D. thesis, University of St. Andrews, Scotland, 2012:

file:///Users/jfpeters/Downloads/RenoLauroPhDThesis.pdf

See page 76, based on Baudrillard 1972 book.

On RG, see the works of S.A. de Groot:

https://www.researchgate.net/profile/Steven_Adriaan_De_Groot

In particular, see

S.A. de Groot, In search of beauty.  Developing beautiful organizations, Ph.D. thesis, Technische Universiteit Endhoven, 2014.

Thank you. These are interesting informal speculations.

Is anyone aware of any formal (in the mathematical sense) Category Theoretic derivations of the emergence of cooperation and organizational adaptation in human interaction dynamics? Perhaps in anthropology or sociology?  My colleagues and I began some discussion in the attached, but we have a long, long way to go.

Article Human Interaction Dynamics (HID): Foundations, Definitions a...

Article Editorial: Human interaction dynamics (hid)-an emerging para...

I would recommend looking at the work of Peter Richerson for an entry point for what social and cultural theorists might have done along the lines you are asking about. I'm not sure if Peter has done anything quite like you suggest, but he'd know if anyone else has:

https://www.researchgate.net/profile/Peter_Richerson

https://www.researchgate.net/profile/Andrzej_Bielecki

My friend Andrzej Bielecki uses category theory in applications of mathematics to biology. It appears that the diagram methods may describe chemical reactions within human body.

Thanks you so much for your interesting answers and history.  

My reason for being interested in the precision of Category Theory is to attempt to make more explicit the many analogies that social scientists have been making to the complexity sciences; complex adaptive systems and emergence are examples. Even more recently, the rise of "social physics" makes these challenges even more obvious.  I was recently asked to offer commentary on a paper that offered the metaphor of thermodynamics to explain human organizing. (See the link below ... or I can send a copy by email if you contact me here: [email protected]) .

After writing the commentary I began to think about how this should be done more rigorously, and the framing of Category theory seems a reasonable approach. 

I'd be happy to explore this with others who actually understand the mathematics.

Article Is this “thermodynamic inquiry” metaphor or more?

Ya, it is true that the wide generality offered in categorical approch is facinating. Currently I am interested in extending various categorical equivalences to various geometries

In addition to my work in category theory (which you seem to be aware of), you might look on my website under Democratic Firms and in my book, Helping People Help Themselves, for non-math treatments of organizational issues.

www.ellerman.org

www.ellerman.org

Thanks David.  In your work, have you applied category theory rigorously to the problem of how human being conceive of themselves (their "concepts of self") as objects as well as how they conceive of others when organizing?  I am intrigued by the role that universal properties (as heuristics) might play in this.

I take the brain functor model more as a way to conceptualize the intentionality of both perception (i.e., "seeing is seeing-as" vs. uninterpreted sense data) and action (i.e., deliberate action vs. just reflex behavior). Universal properties seem to almost always be about starting with heteromorphisms between objects in two different categories and then representing them as homomorphisms inside one of the categories. Both intentional perception and intentional action involve an internal representation of a relation between the organism with the 'brain' and the external environment.

David: Thanks for the above comment.  It took me some reflection (as well as reading some more of your papers) to begin to understand what you are saying. Much is still fuzzy for me, but I see the framing that you describe in the above comment, the brain functor, as a potentially useful way to consider and better understand human organizations, like firms, NGOs and even political systems.  The question would be: How does an organization engage collectively in "perceiving (i.e., 'seeing is seeing-as' vs. uninterpreted sense data) and action (i.e., deliberate action vs. just reflex behavior)."   This is the human organizing problem that I am trying to get my head around.

It seems to me that parsing the objects, relationships and implications using the brain functor as a mathematical model at the level of an organized system like a firm might be useful.  Such a model might offer a way to look for explanations about how efficacious ordering and informational structures within human organizations emerge and stabilize  to provide individual benefits to members of the collective. I have a paper that considers metaphorically how an organization might form a neural network (see below) but there is no mathematical foundation for it.  Do you see any potential here? 

Article Leading large: emergent learning and adaptation in complex s...

I still don't see that the math will be of much help in analyzing organizations. Instead I would recommend these papers one of which is a precis of my 2005 book mentioned before on organizational learning and the other has to do with innovation under genuine uncertainty--which just uses the math duality of series versus parallel to frame the ideas.