Functorial Dynamics and Interaction. Using polynomial functors to model dynamical systems, decision processes, data migration, and more! (I'm completely enthralled with the category Poly.)

A book on the subject is in preparation. Idris code can be found here.

Databases and Networks. This is a 2008 proposal for the first grant I received from the ONR (N000140910466). In it, I propose to use category theory to study databases, networks, and learning. A "summary for the admiral" is here. Here is the final progress report for it.

Networking academia The above ONR grant is in some sense a more technical version of this earlier 2008 proposal, which I had earlier (unsuccessfully) submitted for a grant called "Science and the Human Condition" at the University of Oregon. The idea here is to study networks, as found in computer science, economics, linguistics, sociology, and biology, under a single mathematical framework. The document is written for a layperson. (Unfunded.)

Categorical information theory. This is a 2010 proposal for the second incarnation, N000141010841, of the above ONR grant. Here the focus has shifted to studying systems of information. A final report for this grant can be found here.

Categorical approach to agent interaction. This is a 2012 proposal to use category theory in the study of how agents communicate and interact to form higher-level agents. AFOSR grant number FA9550-14-1-0031.

Categorical informatics. This is a 2013 proposal for the third incarnation of the ONR grant, N000141310260. Here the focus has shifted to some specific problems in databases, such as updates, hierarchy, aggregation, and non-atomic fields. Here are progress reports from 2013 and 2014 and the final report.

Category-theoretic Approaches for the Analysis of Distributed Systems. This is a 2013 proposal (jointly with Honeywell) to use category theory to consider the problem of making high-assurance safety claims on systems composed of smaller systems. NASA grant number NNH13ZEA001N-SSAT. Here is the progress report for year 1. Here is NASA's final review of our work.

Categorical informatics: A functorial approach to data integration This is a proposal for an NSF III grant, submitted November 2015. (Unfunded.)

Solving Information-Integration Problems Using Category Theory. Joint with Ryan Wisnesky (co-PI). This is an NSF I-Corps grant for $50,000 to spend in Spring 2016 in order to find "product-market fit" for the new company Categorical Informatics Inc.

Pixel matrices and other compositional analyses of interconnected systems . This is a 2016 proposal for a funded AFOSR grant to study compositional analysis of systems. AFOSR grant number FA9550-17-1-0058.

Categorical approach to agent interaction: Information, Communication, Planning, and Learning. This is a 2018 proposal for a second incarnation of "Categorical approach to agent interacton". AFOSR grant number FA9550-19-1-0113.

This work by David I. Spivak is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License.