11 citations · 38 across the 12 of their papers we have counts for
12 papers
Topological Quantum Gates in Homotopy Type Theory
David Jaz Myers, Hisham Sati, Urs Schreiber
Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological quantum logic gates had arguably remai…
Orbifolds as microlinear types in synthetic differential cohesive homotopy type theory
David Jaz Myers
Informally, an orbifold is a smooth space whose points may have finitely many internal symmetries. Formally, however, the notion of orbifold has been presented in a number of diffe…
Modal Fracture of Higher Groups
David Jaz Myers
In this paper, we examine the modal aspects of higher groups in Shulman's Cohesive Homotopy Type Theory. We show that every higher group sits within a modal fracture hexagon which…
Behavioral Mereology: A Modal Logic for Passing Constraints
Brendan Fong, David Jaz Myers, David I. Spivak
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by th…
Cartesian Factorization Systems and Grothendieck Fibrations
David Jaz Myers
Every Grothendieck fibration gives rise to a vertical/cartesian orthogonal factorization system on its domain. We define a cartesian factorization system to be an orthogonal factor…
Double Categories of Open Dynamical Systems (Extended Abstract)
David Jaz Myers
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems…
Dirichlet Functors are Contravariant Polynomial Functors
David Jaz Myers, David I. Spivak
Polynomial functors are sums of covariant representable functors from the category of sets to itself. They have a robust theory with many applications -- from operads and opetopes…
A Yoneda-Style Embedding for Virtual Equipments
David Jaz Myers
In this paper, we exhibit a "Yoneda"-style embedding of any virtual equipment into the virtual equipment of categories enriched in it. We show that this embedding preserves composi…
Dirichlet Polynomials form a Topos
David I. Spivak, David Jaz Myers
One can think of power series or polynomials in one variable, such as , as functors from the category of sets to itself; these are known as polynomial…
Good Fibrations through the Modal Prism
David Jaz Myers
Homotopy type theory is a formal language for doing abstract homotopy theory -- the study of identifications. But in unmodified homotopy type theory, there is no way to say that th…
Behavioral Mereology (Proofs and Properties)
Brendan Fong, David Jaz Myers, David I. Spivak
Mereology is the study of parts and the relationships that hold between them. We introduce a behavioral approach to mereology, in which systems and their parts are known only by th…
String Diagrams For Double Categories and Equipments
David Jaz Myers
A popular graphical calculus for monoidal categories makes computations tactile and intuitive. Complicated diagram chases can be expressed in a few pictures and discovered by playi…