Senior Research Scientist and Institute Fellow at
Current research projects
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
Structure and dynamics of working language Using polynomial functors
to account for how language works, in the sense of physics. This grant has been recommended for funding, but has not yet started.
Introductory books on Applied Category theory
Theory for the Sciences was published by MIT Press,
also available on
Here are reviews by
the MAA, by
AMS, and by
Course materials (MIT OCW) can be found
Sketches in Compositionality.
This material has been published by
Cambridge University Press
as An Invitation to Applied Category Theory by
Brendan Fong and David I. Spivak.
This version is free to view and download for personal use only.
Not for re-distribution, re-sale or use in derivative works.
© Brendan Fong and David Spivak 2019. Also available on
Here is a review by the MAA and a review by
Course materials (MIT
OCW) can be found
Past research subjects
Applied Category Theory. Various ACT grants, some funded and others not.
Derived manifolds. The
category of derived manifolds contains arbitrary intersections of
manifolds, even if they are not transverse, while retaining enough
structure so that every compact derived manifold has a fundamental class
Mapping spaces in
quasi-categories. Joint work with Dan Dugger.
High-energy physics. A
paper I coauthored with
Values Statement. This is a first attempt
to convey the values that seem to motivate me.
work by David I. Spivak is licensed under a
Attribution-Share Alike 3.0 Unported License.