Spivak and Robert Kent developed a human-readable categorical system of knowledge representation called
ologs. These were applied, in a series of collaborations with the materials scientist
Markus Buehler, to different problems in materials science. Ologs have been also used by researchers at
NIST. The goal of ologs, and of Spivak's book, was to show that category theory can be made relatively easy and thus be understood by a wider audience.
Piet Hut endorsed the book saying, "This is the first, and so far the only, book to make category theory accessible to non-mathematicians." Spivak has also studied dynamical systems and
operads, originating the operadic approach to wiring diagram syntax. His unpublished work "Metric realization of fuzzy simplicial sets" was cited by the authors of
UMAP as inspirational for that work. Spivak and Brendan Fong wrote a book that summarizes the developments in applied category theory for a wide audience, and started a nonprofit
applied category theory research institute called
Topos Institute, located in Berkeley, California. The two, together with Rémy Tuyeras, wrote the first article using category theory to understand the structure of
deep learning, called "Backprop as functor". Spivak is an editor of a
diamond open access journal,
Compositionality. == Bibliography ==