172 citations · 796 across the 66 of their papers we have counts for
73 papers
Structures on Categories of Polynomials
Brandon T. Shapiro, David I. Spivak
We define the monoidal category of polynomials under composition in any category with finite limits, including both cartesian and vertical morphisms…
All Concepts are
Owen Lynch, Brandon T. Shapiro, David I. Spivak
We show that the double category of comonoids in the category of polynomial functors (previously shown by Ahman-Uustalu and Garner to be equivalent to th…
Dynamic Tracing: a graphical language for rewriting protocols
Kristopher Brown, David I. Spivak
The category Set_* of sets and partial functions is well-known to be traced monoidal, meaning that a partial function S+U -/-> T+U can be coherently transformed into a partial func…
Algebraic Model Management: A Survey
Patrick Schultz, David I. Spivak, Ryan Wisnesky
We survey the field of model management and describe a new model management approach based on algebraic specification.
Duoidal Structures for Compositional Dependence
Brandon T. Shapiro, David I. Spivak
We provide a categorical framework for mathematical objects for which there is both a sort of "independent" and "dependent" composition. Namely we model them as duoidal categories…
Fast Left Kan Extensions Using The Chase
Joshua Meyers, David I. Spivak, Ryan Wisnesky
We show how computation of left Kan extensions can be reduced to computation of free models of cartesian (finite-limit) theories. We discuss how the standard and parallel chase com…