Department of Mathematics
Office: Building 2, Room 180
Current research projects
Proposal: "Pixel matrices and other compositional analyses of
interconnected systems". This is a proposal for another awarded AFOSR
Technical Proposal: "Categorical approach to agent interaction". This is
the proposal for the awarded AFOSR grant FA9550-14-1-0031.
Technical Proposal: Category-theoretic
Approaches for the Analysis of Distributed Systems. This is the
proposal for the awarded NASA grant NNH13ZEA001N-SSAT.
These are several grant proposals, some funded, some in the pipeline,
others not funded, that explain various facets of my research.
What is the underlying mathematical structure of information itself?
FQL. Functorial query
language. Build your own categories, functors, and database
push them around with data migration functors. (Joint
with Ryan Wisnesky).
Category theory book
Press has published "Category theory for the sciences". The book can
also be purchased on
Here are reviews by
the MAA, by
AMS, and by
HTML version: not as nice to read, but
free to the world, on the MIT
Press website. An older
version, entitled "Category theory for scientists", can be found
Past research subjects
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
Category theory for
scientists. Taught at MIT in Spring 2013.
Seven Sketches in
Compositionality. Taught at MIT in Spring 2018, with Brendan Fong.
Dan Dugger's page.
Jacob Lurie's page
John Baez's blog
MIT Math department.
work by David I. Spivak is licensed under a
Attribution-Share Alike 3.0 Unported License.