18 citations · 43 across the 7 of their papers we have counts for
5 papers · 1 filter
Temporal Type Theory: A topos-theoretic approach to systems and behavior
Patrick Schultz, David I. Spivak
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as…
Dynamical Systems and Sheaves
Patrick Schultz, David I. Spivak, Christina Vasilakopoulou
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sor…
Algebraic Databases
Patrick Schultz, David I. Spivak, Christina Vasilakopoulou +1
Databases have been studied category-theoretically for decades. The database schema -- whose purpose is to arrange high-level conceptual entities -- is generally modeled as a categ…
String diagrams for traced and compact categories are oriented 1-cobordisms
David I. Spivak, Patrick Schultz, Dylan Rupel
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The ax…
Regular and exact (virtual) double categories
Patrick Schultz
We propose definitions of regular and exact (virtual) double categories, proving a number of results which parallel many basic results in the theory of regular and exact categories…