6 papers · 1 filter
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…
Learners' Languages
David I. Spivak
In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal func…
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…
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…
Functorial aggregation
David I. Spivak, Richard Garner, Aaron David Fairbanks
We study polynomial comonads and polynomial bicomodules. Polynomial comonads amount to categories. Polynomial bicomodules between categories amount to parametric right adjoint func…
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…