172 citations · 796 across the 66 of their papers we have counts for
6 papers · 1 filter
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…
Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets
Brandon T. Shapiro, David I. Spivak
Natural organized systems adapt to internal and external pressures and this happens at all levels of the abstraction hierarchy. Wanting to think clearly about this idea motivates o…
A reference for categorical structures on
David I. Spivak
In this document, we collect a list of categorical structures on the category of polynomial functors. There is no implied claim that this list is in any way complet…
Collectives: Compositional protocols for contributions and returns
Nelson Niu, David I. Spivak
We introduce a concept called a collective: an interface with a protocol for aggregating contributions and distributing returns. Through such a protocol, many members may participa…
Polynomial Functors and Shannon Entropy
David I. Spivak
Past work shows that one can associate a notion of Shannon entropy to a Dirichlet polynomial, regarded as an empirical distribution. Indeed, entropy can be extracted from any d:Dir…