I’m a research scientist at the Topos Institute in Oxford, UK. My work focuses on categorical systems theory and compositional, conceptual, and collaborative scientific modelling.
I’m generally interested in what it means to be a thing, but particularly interested in (higher) category theory, homotopy type theory, and cohesion. I have been writing a book on categorical systems theory which is currently in its 0th draft — use at your peril (but enjoy)!
I was previously a post-doc working at the Center for Topological and Quantum Systems at NYU Abu Dhabi. I did my PhD with Emily Riehl at Johns Hopkins. My email is my full name (David Jaz Myers) at gmail.
Preprints
___, Mitchell Riley, Commuting Cohesions, arXiv:2301.13780, 2023
___, Orbifolds as Microlinear Types in Synthetic Differential Cohesive HoTT, arXiv:2205.15887, 2022
___, Modal Fracture of Higher Groups, arXiv:2106.15390, 2021
___, A Yoneda-Style Embedding for Virtual Equipments, arXiv:2003.02124, 2020
___ , String Diagrams for Double Categories and Proarrow Equipments, arXiv:1612.02762, 2016
Publications
Math
___, Zyad Hassan, Higher Schreier Theory in Cubical Agda, to appear in the Journal of Symbolic Logic (2024)
___, Hisham Sati, Urs Schreiber Topological Quantum Gates in Homotopy Type Theory, in Communications in Mathematical Physics, arXiv:2303.02382, 2023
___, D. Spivak, Dirichlet Functors are Contravariant Polynomial Functors, in The Graduate Journal of Mathematics (2023), arXiv:2004.04183, 2020
___, Good Fibrations through the Modal Prism, in Higher Structures (2022), arXiv:1908.08034, 2019
___, Double Categories of Open Dynamical Systems (Extended Abstract), arXiv:2005.05956, 2020
D. Spivak, ___, B. Fong, Behavioral Mereology, arXiv:1811.00420, 2018
E. Hanna, C. Lynch, ___, C. Richardson, Finding Intruder Knowledge with Cap Matching, in Guttman J., Landwehr C., Meseguer J., Pavlovic D. (eds) Foundations of Security, Protocols, and Equational Reasoning. Lecture Notes in Computer Science, vol 11565. Springer, Cham.
Other
P. Thibodeau, ___ , S. Flusberg, Similarity-Based Reasoning is Shaped by Recent Learning Experience, in Proceedings of the 38th Annual Conference of the Cognitive Science Society. Austin, TX: Cognitive Science Society. 2016
Notes
___, Cartesian Factorization Systems and Grothendieck Fibrations, arXiv:2006:14022, 2020
D. Spivak, ___, Dirichlet Polynomials Form a Topos, arXiv:2003.04827, 2020
Notes on Homology in Characteristic One, from a course given by Katia Consani (and with material from Emily Riehl) in 2017.
Some Talks and Slides
Tangent Bundles of Spheres, at HoTTEST, 2023, [slides] [video]
Topological Quantum Gates in Homotopy Type Theory, at ACT2023, 2023, [abstract] [slides]
Para Construction as a Wreath Product, at CT2023, 2023, [slides]
Doctrines of Dynamical Systems, at JMM 2023, 2023, [slides]
Orbifolds as Microlinear Spaces, [slides]
Three Realisms and the Idea of Sheaves, at FRA Workshop, 2021, [slides] [video]
Modal Fracture of Higher Groups, at HoTT/UF 2021, [slides]
Modal Fibrations in Homotopy Type Theory, at University of Augsburg, 2021, [slides]
Modal Fibrations in Homotopy Type Theory, at the EPFL Topology Seminar, 2021, [slides]
Modal Fracture of Higher Groups, at the CMU-HoTT Seminar, 2021, [slides]
Paradigms of Composition, at the MIT Category Seminar, 2020, [slides]
Paradigms of Composition, at the Calgary Peripatetic Seminar, 2020, [slides]
Getting equipped for formal category theory, at the Johns Hopkins Category Seminar, 2020
Double categories of Open Dynamical Systems, at ACT 2020, 2020, [video] [slides]
Behavioral Merelogy: a modal logic for passing constraints, at ACT 2020, 2020, [video] [slides]
Higher Schreier Theory, at HoTTEST 2020, 2020, [video] [slides]
Double Categories of Open Dynamical Systems, at the Coimbra Algebra, Logic, and Topology seminar, 2020, [slides]
Homotopy Type Theory for doing Category Theory, at the MIT Category Seminar, 2020, [slides] [video]
Open Dynamical Systems, Trajectories, and Hierarchical Planning, at the MIT Category Seminar, 2020, [video]
A General Definition of Open Dynamical System, at the MIT Category Seminar, 2020, [video]
At a stalk, in general, and other ways of being true, at the Johns Hopkins Category Seminar, 2019, [notes]
A sheaf of rings is a ring of sheaves, and other tales from algebra on the inside, at the Johns Hopkins Category Seminar, 2019, [notes]
Higher Groups in Homotopy Type Theory, for my Oral Exam at JHU, 2019, [slides]
Good Fibrations through the Modal Prism at HoTT 2019, 2019, [slides]
How do you identify one thing with another at Cornell Topology Fesitval, 2019, [slides]
generatingfunctorology, at the Johns Hopkins Category Seminar, 2019
Degrees, Dimensions, and Crispness, at Geometry in Modal HoTT, 2019 [slides] [video]
Logical Topology and Axiomatic Cohesion, at Geometry in Modal HoTT, 2019 [slides] [video]
The logic is coming from inside the category, at the Johns Hopkins Category Seminar, 2018
Towards A¹ Homotopy Type Theory, at the CMU HoTT Seminar, 2018
What is a Thing?, at MIT Categories Seminar, 2018 [slides]
The Yoga of Four Operations, at the Johns Hopkins Category Seminar, 2018
String Diagrams for (Virtual) Proarrow Equipments, at CT 2017, 2017 [slides] [abstract]
Weighted (Co)Limits, at CT 2017 with the Kan Extension Seminar, 2017 [slides]
String Diagrams, Categories, and Enrichment, for Honors thesis requirement at Oberlin, 2016 [slides]
Thinking Recursively, Rethinking Corecursively, for Oberlin Philosophy department, 2015 [slides] [abstract]
Blog Posts
Graphical Regular Logic, with Sophie Libkind, on the n-category Café
A Graphical Calculus for Proarrow Equipments, on the n-Category Café
Gluing Together Finite Shapes with Kelly, on the n-Category Café, written for the Kan Extension Seminar
Enrichment and its Limits, on the n-Category Café, written for the Kan Extension Seminar
History
2022 - now: Postdoc at New York University Abu Dhabi
2017 - 2022: PhD at Johns Hopkins University
2012 - 2017: Oberlin College