I’m a fourth year graduate student at Johns Hopkins University. My advisor is Emily Riehl.

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 teach and TA. Follow this link for more info.

Preprints

___, Modal Fracture of Higher Groups, arXiv:2106.15390 , 2021

___, Double Categories of Open Dynamical Systems (Extended Abstract), arXiv:2005.05956, 2020

___, D. Spivak, Dirichlet Functors are Contravariant Polynomial Functors, arXiv:2004.04183, 2020

___, A Yoneda-Style Embedding for Virtual Equipments, arXiv:2003.02124, 2020

___, Good Fibrations through the Modal Prism, arXiv:1908.08034, 2019

D. Spivak, ___, B. Fong, Behavioral Mereology, arXiv:1811.00420, 2018

___ , String Diagrams for Double Categories and Proarrow Equipments, arXiv:1612.02762, 2016

Publications

Math

Nothing yet.

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.

Talks and Slides

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

2017 - now: Johns Hopkins University

Spring 2015: Central European University

Fall 2015: Budapest Semesters in Mathematics

2012 - 2017: Oberlin College